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Circles and radii

Source: Irish Mathematical Olympiad 2023 Problem 3

May 16, 2023
geometry

Problem Statement

Let A,B,C,D,EA, B, C, D, E be five points on a circle such that ∣AB∣=∣CD∣|AB| = |CD| and ∣BC∣=∣DE∣|BC| = |DE|. The segments ADAD and BEBE intersect at FF. Let MM denote the midpoint of segment CDCD. Prove that the circle of center MM and radius MEME passes through the midpoint of segment AFAF.
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