Why MN is parallel to BC?
Source: JBMO 2003, Problem 3
June 10, 2004
geometrycircumcircleangle bisectorJBMO
Problem Statement
Let , , be the midpoints of the arcs , , on the circumcircle of a triangle not containing the points , , , respectively. Let the line meets and at and , and let be the midpoint of the segment . Let the line meet and at and , and let be the midpoint of the segment .
a) Find the angles of triangle ;
b) Prove that if is the point of intersection of the lines and , then the circumcenter of triangle lies on the circumcircle of triangle .