Question 73
Let $ABCD$ be an isosceles trapezoid with longer base $AB$ such that the bisector of the angle at $D$ passes through $B$. Suppose that the bisector of the angle at $A$ intersects the side $BC$ at the point $P$. Prove that $AB = AP$ if and only if the bisector of $\widehat{PAD}$ passes through $C$.