Problem

Source: Bundeswettbewerb Mathematik 2022, Round 1 - Problem 3

Tags: geometry, tangent, angle bisector, geometry solved, tangent circles, curvilinear incircles



A circle $k$ touches a larger circle $K$ from inside in a point $P$. Let $Q$ be point on $k$ different from $P$. The line tangent to $k$ at $Q$ intersects $K$ in $A$ and $B$. Show that the line $PQ$ bisects $\angle APB$.