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Proving angle equality in a simple configuration

Source: Mexico National Olympiad Mock Exam (OMMock) 2020 P4

November 9, 2020
geometrydiameterperpendicular bisectorvector

Problem Statement

Let ABCABC be a triangle. Suppose that the perpendicular bisector of BCBC meets the circle of diameter ABAB at a point DD at the opposite side of BCBC with respect to AA, and meets the circle through A,C,DA, C, D again at EE. Prove that ∠ACE=∠BCD\angle ACE=\angle BCD.
Proposed by José Manuel Guerra and Victor Domínguez
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