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Concurrence in Cyclic Pentagon

Source: XVII Sharygin Correspondence Round 2021, P15

March 2, 2021
geometryanant mudgal geo

Problem Statement

Let APBCQAPBCQ be a cyclic pentagon. A point MM inside triangle ABCABC is such that ∠MAB=∠MCA\angle MAB = \angle MCA, ∠MAC=∠MBA\angle MAC = \angle MBA and ∠PMB=∠QMC=90∘\angle PMB = \angle QMC = 90^\circ. Prove that AMAM, BPBP, and CQCQ concur.
Anant Mudgal and Navilarekallu Tejaswi
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