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fixed point for constant angle

Source: V Soros Olympiad 1998-99 Round 3 10.10 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics

May 26, 2024
geometryFixed pointfixed

Problem Statement

A chord ABAB is drawn in a circle. The line ℓ\ell is parallel to ABAB and does not intersect the circle. Let CC be a certain point on the circle (points CC located on one side of ABAB are considered). Lines CACA and CBCB intersect ℓ\ell at points DD and EE. Prove that there exists a fixed point FF of the plane, not lying on line ℓ\ell , such that ∠DFE\angle DFE is constant.
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