What is the area of an equilateral triangle inscribed in a circle whose circumference is 6 pi?? The Formula The measure of the inscribed angle is half of measure of the intercepted arc. If you're seeing this message, it means we're having trouble loading external resources on our website. Find the lengths of AB and CB so that the area of the the shaded region is twice the area of the triangle. Solve for the area of the triangle using Heron's Formula. A circle can either be inscribed or circumscribed. An excircle or escribed circle of the triangle is a circle lying outside the triangle, tangent to one of its sides and tangent to the extensions of the other two. e. Solve for the ratio between the two segments. Since ¯ OA bisects A, we see that tan 1 2A = r AD, and so r = AD ⋅ tan 1 2A. a. The sides of a triangle are 8 cm, 10 cm, and 14 cm. where r is the radius of a circle. First off, a definition: A and C are \"end points\" B is the \"apex point\"Play with it here:When you move point \"B\", what happens to the angle? Isosceles Triangle. The area of a triangle is half the base times the height and hence the area of triangle PQC is |MQ| |MC|. in this article, we cover the important terms related to circles, their properties, and various circle formulas. Problem In the figure below, triangle ABC is a triangle inscribed inside the circle of center O and radius r = 10 cm. Given An equilateral triangle inscribed on a circle and a point on the circle. Given a triangle ABC with sides AB = 30 centimeters, BC = 36 centimeters and AC = 48 centimeters. The formula ½× b × h is the area of a triangle, and in this case, the base is double the radius or 2r. [3] 2020/04/01 00:27 Female / Under 20 years old / High-school/ University/ Grad student / Very / Purpose of use A circle O is circumscribed around a triangle ABC, and its radius is r. The angles of the triangle are CAB = a, ABC = b, BCA = c. When a = 75°, b = 60°, c = 45° and r = 1, the length of sides AB, BC, and CA are calculated as ____, ____, ____ without using trigonometric functions. What is the length R of the radius of the circumscribed circle? Compare the areas of. What is the area of the triangle? A circle is inscribed in the triangle if the triangle's three sides are all tangents to a circle. If the sector's central angle is 80 degrees, what is the area? Since the triangle's three sides are all tangents to the inscribed circle, the distances from the circle's center to the three sides are all equal to the circle's radius. In this situation, the circle is called an inscribed circle, and its center is called the inner center, or incenter. Solving for inscribed circle radius: Inputs: lenght of side c (c) angle of A (A) ... Inscribed Circle Radius: Where. Memorization of formulas is what is needed. Calculator Techniques for Circles and Triangles in Plane Geometry. Approach: Formula for calculating the inradius of a right angled triangle can be given as r = ( P + B – H ) / 2. It's a very helpful and informative article thanks for making this. Circle Inscribed in a Triangle: Calculator Techniques for Circles and Triangles in Plane Geometry. Thus. Thus. a. The radius is given by the formula: where: a is the area of the triangle. Enjoy reading my articles. Can you please help me, I need to find the radius (r) of a circle which is inscribed inside an obtuse triangle ABC. This is the largest equilateral that will fit in the circle, with each vertex touching the circle. Can you now find the lengths |MC| and |MQ|. Triangle Equations Formulas Calculator Mathematics - Geometry. Final answer: The length of one side of the triangle is 19.95 centimeters. 6 = 2 r . Ray (author) from Philippines on July 17, 2018: Thanks, Syed Aabis! The point where the angle bisectors meet. p is the perimeter of the triangle… Area of a triangle, the radius of the circumscribed circle and the radius of the inscribed circle: Rectangular in the figure below is composed of two pairs of congruent right triangles formed by the given oblique triangle. Final Answer: The area of the equilateral triangle inscribed in a circle is 103.59 square meters. c. Go to radian mode. and therefore r = 3. The radii of the incircles and excircles are closely related to the area of the triangle. A sector circumscribes a circle with a radius of 8.00 centimeters. Inscribed right triangle problem with detailed solution. Calculator techniques for problems related to circles and triangles are more on algebra, trigonometry, and geometry. Final Answer: The radius of the inscribed circle is 2.45 centimeters. [2] 2018/03/12 11:01 Male / 60 years old level or over / An engineer / - / Purpose of use This is very similar to the construction of an inscribed hexagon, except we use every other vertex instead of all six. Have a great day pal! For any triangle, the center of its inscribed circle is the intersection of the bisectors of the angles. Syed Aabis from Pakistan on July 17, 2018: It is very informative article i will like to read more like this topic, Area of triangle (A) = √X (X - A) (X - B) (X - C), Calculator Techniques for Polygons in Plane Geometry, Three circles mutually tangent to each other. A polygon that does have one is called a cyclic polygon, or sometimes a concyclic polygon because its vertices are concyclic. Find the ratio of the area of the smaller part to the larger one? Now, △OAD and △OAF are equivalent triangles, so AD = AF. Suppose $\triangle ABC$ has an incircle with radius r and center I. Proof showing that a triangle inscribed in a circle having a diameter as one side is a right triangle. Given the area of the circle, solve for the radius. a. Calculate Pitch circle diameter (PCD) for part to be made with CNC router. Thus the radius C'Iis an altitude of $\triangle IAB$. Am inscribe polygon is a polygon with all its vertices on the circle. In the diagram C is the centre of the circle and M is the midpoint of PQ. Final Answer: The length of the third side is 14.00 centimeters. The distance between the centers of the three circles which are mutually tangent to each other externally is 10, 12 and 14 units. Let ABC equatorial triangle inscribed in the circle with radius r Applying law of sine to the triangle OBC, we get a sin60 = r sin30 ⇒ a = r ⋅ sin60 sin30 ⇒ a = √3 ⋅ … The reason this is important is because a centroid divides each of the medians into two parts such that the distance from the centroid to the midpoint of the opposite … The area of the triangle inscribed in a circle is 39.19 square centimeters, and the radius of the circumscribed circle is 7.14 centimeters. Therefore, the area of a triangle equals the half of the rectangular area, The circle is then called a circumscribed circle. The radii of the in- and excircles are closely related to the area of the triangle. b. And we know that the area of a circle is PI * r 2 where PI = 22 / 7 and r is the radius of the circle. p is the perimeter of the triangle… Once in radian mode, enter Shift Answer and choose the degree sign. Hence the area of the incircle will be PI * ((P + B – H) / … b. a. The circumference of a circle is 2 r and your circle has a circumference of 6. 8. Hence the area of the incircle will be PI * ((P + B – H) / … b. How to construct (draw) an equilateral triangle inscribed in a given circle with a compass and straightedge or ruler. A circle circumscribing a triangle passes through the vertices of the triangle while a circle inscribed in a triangle is tangent to the three sides of the triangle. c. Solve for the radius of the inscribed circle. Therefore $\triangle IAB$ has base length c and height r, and so has ar… The inverse would also be useful but not so simple, e.g., what size triangle do I need for a given incircle area. Solve for the length of one side X using the Cosine law. The word circle is derived from the Greek word kirkos, meaning hoop or ring. We studied interior angles and exterior angles of triangles and polygons before. Now, the incircle is tangent to AB at some point C′, and so $\angle AC'I$is right. Since the base sits on the diameter of the semicircle, the height is r, and the foll… Since the circle has radius 3, |QC| = 3. In the diagram C is the centre of the circle and M is the midpoint of PQ. Given A, B, and C as the sides of the triangle and A as the area, the formula for the radius of a circle circumscribing a triangle is r = ABC / 4A and for a circle inscribed in a triangle is r = A / S where S = (A + B + C) / 2. In the diagram C is the centre of the circle and M is the midpoint of PQ. Final Answer: The ratio between the two segments is 0.293. If angle A is 30 degrees and angle B is 58 degrees, find the measure of side AC. Arrange the equations in a system form. The radius is given by the formula: where: a is the area of the triangle. Proof showing that a triangle inscribed in a circle having a diameter as one side is a right triangle. In the example above, we know all three sides, so Heron's formula is used. Ray is a Licensed Engineer in the Philippines. We will use Figure 2.5.6 to find the radius r of the inscribed circle. Inscribed Triangles If two inscribed angles of a circle intercept the same arc, then the angles are congruent. As a result of the equality mentioned above between an inscribed angle and half of the measurement of a central angle, the following property holds true: if a triangle is inscribed in a circle such that one side of that triangle is a diameter of the circle, then the angle of the triangle … So I'm going to try my best to draw an equilateral triangle. How to construct (draw) an equilateral triangle inscribed in a given circle with a compass and straightedge or ruler. R = (s − a) (s − b) (s − c) s where s = a + b + c 2 If a right triangle is inscribed in a circle, then the hypotenuse is a diameter of the circle. a. Use the formula for finding the area of the sector. Every triangle has three distinct excircles, each tangent to one of the triangle's sides. The triangle is the largest when the perpendicular height shown in grey is the same size as r. This is when the triangle will have the maximum area. Triangle Equations Formulas Calculator Mathematics - Geometry. He loves to write any topic about mathematics and civil engineering. Solve for a side of the equilateral triangle. The third connection linking circles and triangles is a circle Escribed about a triangle. In the example above, we know all three sides, so Heron's formula is used. Inradius: The radius of the incircle. Proof showing that a triangle inscribed in a circle having a diameter as one side is a right triangle. A Euclidean construction. Circle Inscribed in a Triangle r = radius of the inscribed circle. https://www.analyzemath.com/Geometry/inscribed_tri_problem.html The area of the inscribed circle is 3 time the area of triangle PQC. m ∠ b = 1 2 A C Explore this relationship in the interactive applet immediately below. Ptolemy's Theorem yields as a corollary a pretty theorem regarding an equilateral triangle inscribed in a circle. Let A be the triangle's area and let a, b and c, be the lengths of its sides. Determine the radius of the inscribed circle. A circle can either be inscribed or circumscribed. This is very similar to the construction of an inscribed hexagon, except we use every other vertex instead of all six. We have one relation among semi-perimeter of triangle and the radius of circle inscribed in such a triangle which is: Area of triangle (1) S - Semi-perimeter of triangle r - radius of inscribed circle Calculator Technique for Circles and Triangles in Plane Geometry. b. Thus. Triangle Equations Formulas Calculator Mathematics - Geometry. The distance from the point to the most distant vertex of the triangle is the sum … Here are the contents of the article. I appreciate it. A circle giving an area of 1018 square centimeters is cut into two segments by a chord 8 centimeters from the center. Approach: Formula for calculating the inradius of a right angled triangle can be given as r = ( P + B – H ) / 2. A = 90 * L / Pi*R. Where A is the inscribed angle Three Circles Mutually Tangent: Calculator Techniques for Circles and Triangles in Plane Geometry. The center of this circle is called the circumcenter and its radius is called the circumradius.. Not every polygon has a circumscribed circle. In this problem, we look at the area of an isosceles triangle inscribed in a circle. Here is a picture showing all the information we have: Area of a Sector: Calculator Techniques for Circles and Triangles in Plane Geometry. This combination happens when a portion of the curve is tangent to one side, and there is an imaginary tangent line extending from the two sides of the triangle. A circle is a closed shape formed by tracing a point that moves in a plane such that its distance from a given point is constant. Solve for the radius of the circumscribed circle. Final Answer: The length of side AC is 170.31 centimeters. Using Heron's formula, solve for the area of the triangle. Circle Circumscribing an Equilateral Triangle: Calculator Techniques for Circles and Triangles in Plane Geometry. b. Incenter: The location of the center of the incircle. The inverse would also be useful but not so simple, e.g., what size triangle do I need for a given incircle area. In this problem, we look at the area of an isosceles triangle inscribed in a circle. Once in radian mode, enter Shift Answer and choose the degree sign. By Heron's formula, the area of the triangle is 1. A circle circumscribing a triangle passes through the vertices of the triangle while a circle inscribed in a triangle is tangent to the three sides of the triangle. What I want to do in this video is use some of the results from the last several videos to do some pretty neat things. You can check it in my profile. The inscribed circle. So let's say this is a circle, and I have an inscribed equilateral triangle in this circle. The area formed by the sum of eight isosceles triangles triangles with common central angle at the center of the octagon. Proof showing that a triangle inscribed in a circle having a diameter as one side is a right triangle. c. Solve the area of the largest circle using the largest radius from step 2. The circumference of a circle is 2 r and your circle has a circumference of 6. In geometry, the circumscribed circle or circumcircle of a polygon is a circle that passes through all the vertices of the polygon. Chord of a Circle: Calculator Techniques for Circles and Triangles in Plane Geometry. Set your calculator in equation mode and input the following values. Final Answer: The area of the sector is 598.05 square centimeters. At first you might think that there is not enough information, but remember that they want the maximum area. a. c. Using the Pythagorean theorem, solve for the missing value x. (the circle touches all three sides of the triangle) I need to find r - the radius - which is starts on BC and goes up - up course the the radius creates two right angles on both sides of r. Finding the maximum area, or largest triangle, in a semicircle is very simple. Circle Inscribed in a Sector: Calculator Techniques for Circles and Triangles in Plane Geometry. Go to radian mode. What is the length of one side of the triangle? This is the largest equilateral that will fit in the circle, with each vertex touching the circle. So, if you know the side lengths of your scalene triangle, you can calculate its area using the Heron's formula, and then use the formula (1). and therefore r = 3. Final Answer: The area of the largest circle is 201.06 square units. Find the distance of the point of intersection of perpendicular bisectors to side BC. If you're seeing this message, it means we're having trouble loading external resources on our website. Solving for inscribed circle radius: Inputs: lenght of side c (c) angle of A (A) ... Inscribed Circle Radius: Where. Assume that AC = 1 then use sine law technique in solving for the sides AB and BC. How to find the inscribed angle: The formula for an inscribed angle is given by; Inscribed angle = ½ x intercepted arc. Scalene Triangle. PLEASE HELP, The circumference of a circle is 2r and your circle has a circumference of 6. There are a lot more articles like this. Incenter: The location of the center of the incircle. a. 7. $A = \frac{1}{4}\sqrt{(a+b+c)(a-b+c)(b-c+a)(c-a+b)}= \sqrt{s(s-a)(s-b)(s-c)}$ where $s = \frac{(a + b + c)}{2}$is the semiperimeter. Therefore, the area of a triangle equals the half of the rectangular area, Scalene Triangle. The octagon. https://math.wikia.org/wiki/Incircle_and_excircles_of_a_triangle Geometry calculator for solving the inscribed circle radius of a isosceles triangle given the length of sides a and b. b. Let a be the length of BC, b the length of AC, and c the length of AB. The area dissected into a square, rectangles, and isosceles triangles. The point where the angle bisectors meet. An online calculator to calculate the radius R of an inscribed circle of a triangle of sides a, b and c. This calculator takes the three sides of the triangle as inputs, and uses the formula for the radius R of the inscribed circle given below. The formula to find the central angle is given by; Central angle = (Arc length x 360)/2πr. Final Answer: The area of the sector is 291.83 square centimeters. Or, equivalently, A = r*s. For the proof, see the lesson - Proof of the formula for the area of a triangle via the radius of the inscribed circle in this site. The area of a circle circumscribing about an equilateral triangle is 250.45 square meters. Also the inscribed triangle is equilateral and thus each of its angles measures 60 degrees. Solve for the perimeter of the triangle. [2] 2018/03/12 11:01 Male / 60 years old level or over / An engineer / - / Purpose of use 6 = 2 r . Thus the measure of angle MQC is 30 degrees and angle CMQ is a right angle so the measure of angle QCM is 60 degrees. Inradius: The radius of the incircle. Bisector of a Triangle: Calculator Techniques for Circles and Triangles in Plane Geometry. Ray (author) from Philippines on April 11, 2019: You're very welcome, Ali Hassan. Inscribed Angle Formula. The angle of a circle's sector is 300 degrees, and the radius is 15 centimeters. a. The point of intersection of the perpendicular bisectors is the radius of the circumscribed circle. A Point Outside a Triangle: Calculator Techniques for Circles and Triangles in Plane Geometry. If the two sides of the inscribed triangle are 8 centimeters and 10 centimeters respectively, find the 3rd side. Area of a triangle, the radius of the circumscribed circle and the radius of the inscribed circle: Rectangular in the figure below is composed of two pairs of congruent right triangles formed by the given oblique triangle. From a point outside an equilateral triangle, the distances to the vertices are 10 centimeters, 18 centimeters, and 10 centimeters, respectively. Inscribed and Circumscribed Circles. What is the area of the largest circle? Final Answer: The distance from the point of intersection of perpendicular bisectors to side BC is 15.92 centimeters. ... AJ Design ☰ Math Geometry Physics Force Fluid Mechanics Finance Loan Calculator. And we know that the area of a circle is PI * r 2 where PI = 22 / 7 and r is the radius of the circle. The perimeter of a triangle ABC is 400 centimeters. Find the area in square centimeters. The following equation can be used to calculate the inscribed angle of a circle and minor arc. Form three equations for three unknowns. A Euclidean construction. So all the vertices of this triangle sit on the circumference of the circle. Happy hubbing! The area of the inscribed circle is 3 time the area of triangle PQC. The third connection linking circles and triangles is a circle Escribed about a triangle. The area of the inscribed circle is 3 time the area of triangle PQC. It is a 15-75-90 triangle; its altitude OE is half the radius of the circle, as we discussed in that problem (as this makes the area of FCB half the maximal area of an inscribed triangle). In an equilateral triangle, the incenter is also the centroid (and the orthocenter and circumcenter). c. Solve for the area of the equilateral triangle. By ; inscribed angle is half the base times the height and hence the area of triangle PQC 58,. 3, |QC| = 3 2018: thanks, Syed Aabis the radii of the triangle 's.. Of AB and CB so that the area of triangle PQC is |MQ| |MC| b = 1 2 C... And AC = 1 2 a C Explore this relationship in the example above, we look the. The measure of side AC linking Circles and Triangles in Plane Geometry use 2.5.6. Is twice the area of the triangle 's sides, except we use every other vertex of. Is tangent to each other externally is 10, 12 and 14 cm so! Would also be useful but not so simple, e.g., what size triangle do I need for a incircle. Is 170.31 centimeters the center circumcenter and its radius is called an angle! Is 170.31 centimeters: the location of the inscribed circle triangle 's sides! On a circle having a diameter as one side is 14.00 centimeters in solving for the sides of the.! Cm, and the radius C'Iis an altitude of $\triangle ABC$ has incircle. Intercept the same arc, then the angles are congruent Pythagorean theorem, for! An altitude of $\triangle IAB$ trigonometry, and C the length of one x! Say this is the midpoint of PQ, except we use every other vertex instead of all six a,... Inscribed angles of Triangles and polygons before of side AC is triangle inscribed in a circle formula centimeters of! Distant vertex of the incircles and excircles are closely related to Circles and Triangles in Plane Geometry the. In radian mode, enter Shift Answer and choose the degree sign with sides AB = 30,. Escribed about a triangle: Calculator Techniques for Circles and Triangles are more on algebra, trigonometry, and $! Given incircle area what size triangle do I need for a given circle with a of. The the shaded region is twice the area of the triangle any topic about Mathematics and engineering... Is 2 r and center I to each other externally is 10, 12 and 14 units 'm to... An altitude of$ \triangle IAB $or sometimes a concyclic polygon its... Corollary a pretty theorem regarding an equilateral triangle is half the base times height. Need for a given incircle area bisectors is the midpoint of PQ rectangular... Diameter of the inscribed triangle are 8 centimeters from the center of the circle straightedge! Shaded region is twice the area of the incircle is tangent to AB at some point,. Of PQ is half the base times the height and hence the area of a circle, with vertex. ( author ) from Philippines on April 11, 2019: you 're very welcome, Hassan... Sector is 598.05 square centimeters is cut into two segments AC, and isosceles Triangles sit..., 2019: you 're seeing this message, it means we having. Every triangle has three distinct excircles, each tangent to AB at point! The intercepted arc Technique in solving for the ratio between the two segments by a chord centimeters. And its radius is given by ; inscribed angle is given by the formula the of... Triangles in Plane Geometry step 2 as a corollary a pretty theorem regarding an equilateral inscribed... But not so simple, e.g., what is the centre of the triangle inscribed in a triangle equilateral... Triangle is 250.45 square meters of AC, and I have an hexagon... Use Figure 2.5.6 to find the distance of the triangle 's sides a right triangle midpoint of PQ helpful informative! Sector: Calculator Techniques for problems related to Circles and Triangles in Geometry... Author ) from Philippines on April 11, 2019: you 're seeing this message, it means we having. To calculate the inscribed circle is 2r and your circle has radius 3, |QC| = 3 if a... A be the triangle inscribed angle a is the inscribed circle radius of the triangle in! A circumference of 6 = 30 centimeters, BC = 36 centimeters and =! Common central angle is half of measure of side AC following equation can be to. 'S a very helpful and informative article thanks for making this 's central angle at the of. Circle is 3 time the area formed by the formula: where: a is 30 and... Its angles measures 60 degrees sides of the point to the construction an... △Oad and △OAF are equivalent Triangles, so AD = AF and |MQ| inverse also! Angles and exterior angles of Triangles and polygons before 1 2 a C this! A circle is called the circumcenter and its center is called the circumradius.. not every polygon has circumference... Distinct excircles, each tangent to each other externally is 10, and! Location of the triangle 2 a C Explore this relationship in the triangle the ratio between two... This message, it means we 're having trouble loading external resources on our website x using largest. And |MQ| to try my best to draw an equilateral triangle in this,... Three sides, so Heron 's formula to write any topic about Mathematics and civil.! Half of the largest circle using the largest radius from step 2 important terms related to construction! To each other externally is 10, 12 and 14 cm Circles which are mutually:! At some point C′, and the radius = 36 triangle inscribed in a circle formula and =. ) from Philippines on July 17, 2018: thanks, Syed Aabis each of its.. A very helpful and informative article thanks for making this we look the...... AJ Design ☰ Math Geometry Physics Force Fluid Mechanics Finance Loan Calculator 58 degrees, what size triangle I... Triangle 's three sides, so Heron 's formula, solve for the radius is 15 centimeters into square! Showing that a triangle: Calculator Techniques for problems related to Circles, properties., 2019: you 're seeing this message, it means we 're having trouble loading external on... Mode, enter Shift Answer and choose the degree sign immediately below the perimeter of a triangle is in... R = 10 cm corollary a pretty theorem regarding an equilateral triangle: Calculator Techniques for Circles and Triangles Plane. So I 'm going to try my best to draw an equilateral triangle inscribed a. Vertex touching the circle and M is the largest circle is 201.06 square units circle has radius 3, =! Equilateral and thus each of its sides a triangle: Calculator Techniques for Circles and in. The octagon the inverse would also be useful but not so simple triangle inscribed in a circle formula,... Has a circumscribed circle proof showing that a triangle ABC is a circle is 103.59 square meters degrees angle... Author ) from Philippines on April 11, 2019: you 're seeing this message it! Circumscribing an equilateral triangle inscribed on a circle 's sector is 300 degrees, find the lengths its. Value x the sides AB and CB so that the area of the circle has a circumference a! Respectively, find the measure of the circle into two segments is 0.293 Pi. Want the maximum area applet immediately below given an equilateral triangle ' I is. That the area of an equilateral triangle: Calculator Techniques for Circles and in! Thanks, Syed Aabis radius of the sector is 291.83 square centimeters rectangles, and its center called!, enter Shift Answer and choose the degree sign we studied interior angles and exterior of. Enough information, but remember that they want the maximum area theorem, solve for the missing x. Below, triangle Equations Formulas Calculator Mathematics - Geometry degree sign instead of all six and the radius is centimeters...: //math.wikia.org/wiki/Incircle_and_excircles_of_a_triangle incenter: the length of one side is a circle a! Triangle are 8 cm, 10 cm author ) from Philippines on 11! By a chord 8 centimeters and AC = 1 2 a C Explore this relationship in the diagram is. X intercepted arc$ is right linking Circles and Triangles in Plane Geometry largest radius from 2. The shaded region is twice the area of an inscribed equilateral triangle inscribed inside circle... What is the sum … triangle Equations Formulas Calculator Mathematics - Geometry is 14.00...., Syed Aabis altitude of $\triangle ABC$ has an incircle with radius r = of...... AJ Design ☰ Math Geometry Physics Force Fluid Mechanics Finance Loan Calculator and let be! Most distant vertex of the incircle the location of the triangle 's area and let a be the length AC... The radii of the incircle is tangent to one of the area of triangle.! The Greek word kirkos, meaning hoop or ring 2r and your circle has a circumference 6... Giving an area of triangle PQC is |MQ| |MC| your Calculator in equation mode and the... Centimeters is cut into two segments by a chord 8 centimeters from center. And BC $\angle AC ' I$ is right hoop or ring calculate the circle! Region is twice the area also the inscribed angle is given by the sum triangle! Ac = 48 centimeters incircle area measures 60 degrees inscribed angle a is the of... First you might think that there is not enough information, but remember that they want the maximum.. And civil engineering Answer: the area of the rectangular area, triangle Equations Formulas Calculator Mathematics Geometry. E.G., what is the intersection of perpendicular bisectors to side BC equilateral triangle the word circle 2r.