MathDB
Varying circle through a vertex and the incenter and a fixed angle

Source: Bulgarian Spring Tournament 2024 10.2

March 31, 2024
geometry

Problem Statement

Let ABCABC be a triangle and a circle ω\omega through CC and its incenter II meets CA,CBCA, CB at P,QP, Q. The circumcircles (CPQ)(CPQ) and (ABC)(ABC) meet at LL. The angle bisector of ∠ALB\angle ALB meets ABAB at KK. Show that, as ω\omega varies, ∠PKQ\angle PKQ is constant.
Back to ProblemsView on AoPS