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Midpoints and equal angles

Source: Cyprus 2021Junior TST-3 Problem 4

May 19, 2021
geometry

Problem Statement

Let △ABΓ\triangle AB\varGamma be an acute-angled triangle with AB<AΓAB < A\varGamma, and let OO be the center of the circumcircle of the triangle. On the sides ABAB and AΓA \varGamma we select points TT and PP respectively such that OT=OPOT=OP. Let M,KM,K and Λ\varLambda be the midpoints of PT,PBPT,PB and ΓT\varGamma T respectively. Prove that ∠TMK=∠MΛK\angle TMK = \angle M\varLambda K.
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