two intersecting circles, prove that a line bisects a segment
Source: 2012 Sharygin Geometry Olympiad Final Round 10.7
August 3, 2018
geometrycirclesbisection
Problem Statement
Consider a triangle . The tangent line to its circumcircle at point meets line at point . The tangent lines to the circumcircle of triangle at points and meet at point . Prove that line bisects segment .(F.Ivlev)