MathDB
2017 IGO Intermediate P5

Source: 4th Iranian Geometry Olympiad (Intermediate) P5

September 15, 2017
IGOIrangeometrycircumcircle

Problem Statement

Let X,YX,Y be two points on the side BCBC of triangle ABCABC such that 2XY=BC2XY=BC (XX is between B,YB,Y). Let AA′AA' be the diameter of the circumcirle of triangle AXYAXY. Let PP be the point where AXAX meets the perpendicular from BB to BCBC, and QQ be the point where AYAY meets the perpendicular from CC to BCBC. Prove that the tangent line from A′A' to the circumcircle of AXYAXY passes through the circumcenter of triangle APQAPQ.
Proposed by Iman Maghsoudi
Back to ProblemsView on AoPS