Let $P$ be a point on the median $AM$ of a triangle $ABC$. Suppose that the tangents to the circumcircles of $ABP$ and $ACP$ at $B$ and $C$ respectively meet at $Q$. Show that $\angle PAB = \angle CAQ$.
Source: 2018 Pan-African Shortlist - G2
Tags: geometry, Tangents, Triangle
Let $P$ be a point on the median $AM$ of a triangle $ABC$. Suppose that the tangents to the circumcircles of $ABP$ and $ACP$ at $B$ and $C$ respectively meet at $Q$. Show that $\angle PAB = \angle CAQ$.