MathDB
Geometry from EGMO 2018

Source: EGMO 2018 P1

April 11, 2018
geometryEGMOTrianglecircleEGMO 2018

Problem Statement

Let ABCABC be a triangle with CA=CBCA=CB and ∠ACB=120∘\angle{ACB}=120^\circ, and let MM be the midpoint of ABAB. Let PP be a variable point of the circumcircle of ABCABC, and let QQ be the point on the segment CPCP such that QP=2QCQP = 2QC. It is given that the line through PP and perpendicular to ABAB intersects the line MQMQ at a unique point NN. Prove that there exists a fixed circle such that NN lies on this circle for all possible positions of PP.
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