Let $ABC$ be such a triangle, that $AB = 3\cdot BC$. Points $P$ and $Q$ lies on the side $AB$ and $AP = PQ = QB$. A point $M$ is the midpoint of the side $AC$. Prove that $\sphericalangle PMQ = 90^{\circ}$.
Source: Polish Junior MO 2019 Second Round
Tags: geometry
Let $ABC$ be such a triangle, that $AB = 3\cdot BC$. Points $P$ and $Q$ lies on the side $AB$ and $AP = PQ = QB$. A point $M$ is the midpoint of the side $AC$. Prove that $\sphericalangle PMQ = 90^{\circ}$.
