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MP = MQ, 2 circumcircles related

Source: Estonia IMO TST 2014 p4

April 5, 2020
geometrycircumcircleequal segmentsaltitudes

Problem Statement

In an acute triangle the feet of altitudes drawn from vertices AA and BB are DD and EE, respectively. Let MM be the midpoint of side ABAB. Line CMCM intersects the circumcircle of CDECDE again in point PP and the circumcircle of CABCAB again in point QQ. Prove that ∣MP∣=∣MQ∣|MP| = |MQ|.
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