MathDB
All lines PQ concur

Source: Sharygin 2022 P17

March 4, 2022
geometry

Problem Statement

Let a point PP lie inside a triangle ABCABC. The rays starting at PP and crossing the sides BCBC, ACAC, ABAB under the right angle meet the circumcircle of ABCABC at A1A_{1}, B1B_{1}, C1C_{1} respectively. It is known that lines AA1AA_{1}, BB1BB_{1}, CC1CC_{1} concur at point QQ. Prove that all such lines PQPQ concur.