symmedian wanted, starting with intersecting circles
Source: 2009 Oral Moscow Geometry Olympiad grades 10-11 p6
September 14, 2020
geometrysymmediancircles
Problem Statement
To two circles and , intersecting at points and , their common tangent is drawn ( and are tangency points, respectively, point is closer to line than ). Line passing through , intersects and for second time at points and , respectively ( lies between and ). Lines and intersect at point . Prove that is the symmedian of triangle .(Yu. Blinkov)