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NIce geometry

Source: Bosnia Herzegovina TST 2017, problem 6

July 24, 2017
geometrycircumcircle

Problem Statement

Given is an acute triangle ABCABC. MM is an arbitrary point at the side ABAB and NN is midpoint of ACAC. The foots of the perpendiculars from AA to MCMC and MNMN are points PP and QQ. Prove that center of the circumcircle of triangle PQNPQN lies on the fixed line for all points MM from the side ABAB.
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