ASU 170 All Soviet Union MO interior point isosceles triangles with all vertices
Source:
July 3, 2019
isoscelesgeometry
Problem Statement
The point inside the convex polygon makes isosceles triangle with all the pairs of its vertices. Prove that is the centre of the circumscribed circle.other formulation:
is a convex polygon and is an interior point such that for every pair of vertices , the triangle is isosceles. Prove that all the vertices of lie on a circle with center .