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equilateral wanted, right isosceles (2019 Romania District VII p4)

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May 22, 2020
geometryEquilateralright triangleisosceles

Problem Statement

Consider the isosceles right triangleABC,∠A=90o ABC, \angle A = 90^o, and point D∈(AB)D \in (AB) such that AD=13ABAD = \frac13 AB. In the half-plane determined by the line ABAB and point CC , consider a point EE such that ∠BDE=60o\angle BDE = 60^o and ∠DBE=75o\angle DBE = 75^o. Lines BCBC and DEDE intersect at point GG, and the line passing through point GG parallel to the line ACAC intersects the line BEBE at point HH. Prove that the triangle CEHCEH is equilateral.
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