SHARYGIN 2021 Problem 15

Let $APBCQ$ be a cyclic pentagon. A point $M$ inside triangle $ABC$ is such that $\angle MAB = \angle MCA$ , $\angle MAC = \angle MBA$ and $\angle PMB = \angle QMC = 90^\circ$ . Prove that $AM$ , $BP$ , and $CQ$ concur.

Anant Mudgal and Navilarekallu Tejaswi