MathDB
fixed point for Russian 9graders

Source: Sharygin Geometry Olympiad 2015 Final 9.4

August 1, 2018
geometryFixed point

Problem Statement

A fixed triangle ABCABC is given. Point PP moves on its circumcircle so that segments BCBC and APAP intersect. Line APAP divides triangle BPCBPC into two triangles with incenters I1I_1 and I2I_2. Line I1I2I_1I_2 meets BCBC at point ZZ. Prove that all lines ZPZP pass through a fixed point.
(R. Krutovsky, A. Yakubov)
Back to ProblemsView on AoPS