Three circles passing through X...
Source: Tournament of towns, Senior B-Level paper, Fall 2004
December 25, 2004
geometrygeometry solved
Problem Statement
Three circles pass through point X. Their intersection points (other than X) are denoted A, B, C. Let A' be the second point of intersection of line AX and the circle circumscribed around triangle BCX, and define similarly points B', C'. Prove that triangles ABC', AB'C, and A'BC are similar.