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Incredible vanilla geometry again

Source: INMO 2021 Problem 5

March 7, 2021
geometryanglesEquilateral Triangleequal lengthsINMOtrigonometry

Problem Statement

In a convex quadrilateral ABCDABCD, ∠ABD=30∘\angle ABD=30^\circ, ∠BCA=75∘\angle BCA=75^\circ, ∠ACD=25∘\angle ACD=25^\circ and CD=CBCD=CB. Extend CBCB to meet the circumcircle of triangle DACDAC at EE. Prove that CE=BDCE=BD.
Proposed by BJ Venkatachala
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