Question 5
Let $ABCD$ be a convex cyclic quadrilateral. Put $E=AC\cap BD$, $F=AB\cap CD$, $G=DA\cap BC$. Circle $ABE$ meets line $CB$ again at $P$, and circle $ADE$ meets line $CD$ again at $Q$. Suppose the orders are $C,B,P,G$ and $C,Q,D,F$. Put $M=FP\cap GQ$. Prove $\angle MAC=90^\circ$.
Proposed by Kada Williams. Source: Evan Chen’s third-party compilation, not an official publication. One editorial point; manual grading only.
Proposed by Kada Williams. Source: Evan Chen’s third-party compilation, not an official publication. One editorial point; manual grading only.