Question 4
Let $ABCD$ be a cyclic quadrilateral. Let $P$, $Q$ and $R$ be the feet of perpendiculars from $D$ to lines $\overline{BC}$, $\overline{CA}$ and $\overline{AB}$, respectively. Show that $PQ = QR$ if and only if the bisectors of angles $ABC$ and $ADC$ meet on segment $\overline{AC}$.