MathDB
The Wrong Problem

Source: Germany TST 2012 P2

April 13, 2020
geometrycircumcircle

Problem Statement

Let Γ\Gamma be the circumcircle of isosceles triangle ABCABC with vertex CC. An arbitrary point MM is chosen on the segment BCBC and point NN lies on the ray AMAM with MM between A,NA,N such that AN=ACAN=AC. The circumcircle of CMNCMN cuts Γ\Gamma in PP other than CC and AB,CPAB,CP intersect at QQ. Prove that ∠BMQ=∠QMN.\angle BMQ = \angle QMN.
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