Question 8
Point $D$ is chosen on side $BC$ of the acute triangle $ABC$ so that $AD = AC$. Let $P$ and $Q$ be respectively the feet of the perpendiculars from $C$ and $D$ to $\overline{AB}$. It is known that
$$AP^2 + 3BP^2 = AQ^2 + 3BQ^2.$$ Find $\hat{A}BC$.
$$AP^2 + 3BP^2 = AQ^2 + 3BQ^2.$$ Find $\hat{A}BC$.