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Altitudes and midpoints. Prove that 4 points are concyclic.

Source: St. Petersburg MO 2000, 9th grade, P2

April 22, 2023
geometryAngle ChasingSt. Petersburg MO

Problem Statement

Let AA1AA_1 and CC1CC_1 be altitudes of acute angled triangle ABCABC. A point DD is chosen on AA1AA_1 such that A1D=C1DA_1D=C_1D. Let EE be the midpoint of ACAC. Prove that points AA, C1C_1, DD, EE are concylic.
[I]Proposed by S. Berlov
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