Problem

Source: Ukraine MO 2021 8.4

Tags: geometry



Let $ABC$ be an isosceles triangle with $AB = AC$. Points $P$ and $Q$ inside $\triangle ABC$ are such that $\angle BPC = \frac{3}{2} \angle BAC$, $BP = AQ$ and $AP = CQ$. Prove that $AP = PQ$. Proposed by Fedir Yudin