MathDB
Two circles and midpoints of arcs

Source: Romania EGMO TST 2021 Day 1 P2

November 23, 2022
geometryromania

Problem Statement

Two circles intersect at points A≠BA\neq B. A line passing through AA{} intersects the circles again at CC and DD. Let EE and FF be the midpoints of the arcs \overarc{BC} and \overarc{BD} which do not contain AA{} and let MM be the midpoint of the segment CDCD. Prove that MEME and MFMF are perpendicular.
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