MathDB
RMO 2023 P2

Source:

October 29, 2023
geometry

Problem Statement

Let ω\omega be a semicircle with ABA B as the bounding diameter and let CDC D be a variable chord of the semicircle of constant length such that C,DC, D lie in the interior of the arc ABA B. Let EE be a point on the diameter ABA B such that CEC E and DED E are equally inclined to the line ABA B. Prove that (a) the measure of ∠CED\angle C E D is a constant; (b) the circumcircle of triangle CEDC E D passes through a fixed point.
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