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A rather famous lemma in geometry

Source: Bundeswettbewerb Mathematik 2022, Round 1 - Problem 3

March 30, 2022
geometrytangentangle bisectorgeometry solvedtangent circlescurvilinear incircles

Problem Statement

A circle kk touches a larger circle KK from inside in a point PP. Let QQ be point on kk different from PP. The line tangent to kk at QQ intersects KK in AA and BB. Show that the line PQPQ bisects ∠APB\angle APB.
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