MathDB
vertex reflection concyclic with line joining foots

Source: Sharygin 2023 - P16 (Grade-9-11)

March 4, 2023
geometryreflectionaltitudesSharygin Geometry OlympiadSharygin 2023

Problem Statement

Let AHAAH_A and BHBBH_B be the altitudes of a triangle ABCABC. The line HAHBH_AH_B meets the circumcircle of ABCABC at points PP and QQ. Let A′A' be the reflection of AA about BCBC, and B′B' be the reflection of BB about CACA. Prove that A′,B′,P,QA',B', P,Q are concyclic.
Back to ProblemsView on AoPS