# Van Khea: Cyclic R,A,Q,C:

Let $I$ be incenter of $\Delta ABC$. Let $BI$ cut circumcircle of $\Delta ABC$ at $D$. Let $P=AP\perp BC$ and $Q\in PC$ such that $BP=PQ$. The circumcircle of $\Delta BQD$ cut $BA$ at $R$. Prove that $R, A, Q, C$ are cyclic if and only if $\angle B=60^0$.