IMO 2003 Problem 4

Let $ABCD$ be a cyclic quadrilateral. Let $P$ , $Q$ , $R$ be the feet of the perpendiculars from $D$ to the lines $BC$ , $CA$ , $AB$ , respectively. Show that $PQ=QR$ if and only if the bisectors of $\angle ABC$ and $\angle ADC$ are concurrent with $AC$ .

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