Equilateral triangle within a circumscribed circle. In the attached picture there is an equilateral triangle within a circumscribed circle. All three angles are equal to 60 degrees. Most commonly we find the symbol as a circumscribed triangle, which is an equilateral triangle within and touching a circle at each vertex, but there are other occasions when the triangle is placed well inside the circle and not touching the sides. Circumscribed circle of an equilateral triangle is made through the three vertices of an equilateral triangle. Equilateral triangle Known value The length of the sides The area The perimeter The radius of the circumscribed circle The radius of the inscribed circle The altitude or height The length of the sides Law of Cosines. length of side a. angle of A. Equilateral Triangle: All three sides have equal length. radius of the circumscribed circle of an equilateral triangle : = Digit 2 1 2 4 6 10 F. =. Equilateral Triangle … radius of the circumscribed circle of an equilateral triangle : = Digit 2 1 2 4 6 10 F. =. I wish to prove that MT = TW, i.e., that the triangle's edge cuts the radius into equal parts. MW is a radius of the circle. Inscribed Circle Radius. Equilateral triangles are the simplest regular polygons. Given an equilateral triangle ABC and point M, the centroid, when joining points A, B, M, C, A, constructs a  concave quadrilateral symmetrical  with respect to bisector A, with vertex M of the entering angle; the diagonal AM inside the quadrilateral and BC, diagonal outside the polygon. Circumscribed Circle Radius. The radius of a circumcircle of an equilateral triangle is equal to (a / √3), where ‘a’ is the length of the side of equilateral triangle.