equal segments and equilateral triangle
Source: Vietnam NMO 1999, problem 2
September 6, 2008
geometrycircumcirclegeometry proposed
Problem Statement
let a triangle ABC and A',B',C' be the midpoints of the arcs BC,CA,AB respectively of its circumcircle. A'B',A'C' meets BC at respectively. Pairs of point are similarly defined. Prove that A_1A_2 \equal{} B_1B_2 \equal{} C_1C_2 if and only if triangle ABC is equilateral.