Question 19
Let $ABC$ be an equilateral triangle with circumcentre $O$. Let $P$ be a point inside the triangle such that $\angle BPC = 120^\circ$ and $P \ne O$. Let $B'$ and $C'$ be the images of $B$ and $C$ respectively under the reflection in the line $PO$. Furthermore $B'C'$ meets $AP$ at $D$. Determine $AD : DP$. Justify your claim.