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isosceles wanted, symmetric wrt BC lies on circumcircle

Source: 2017 Portugal p2

October 11, 2020
geometrySymmetricisoscelescircumcircle

Problem Statement

In triangle [ABC][ABC], the bisector in CC and the altitude passing through BB intersect at point DD. Point EE is the symmetric of point DD wrt BCBC and lies on the circle circumscribed to the triangle [ABC][ABC]. Prove that the triangle is [ABC][ABC] isosceles.
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