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Geometry with 18 degree

Source: Azerbaijan NMO 2016. Senior P2

July 27, 2023
geometry

Problem Statement

On the extension of the hypotenuse ABAB of the right-angled triangle ABCABC, the point DD after the point B is marked so that DC=2BCDC = 2BC. Let the point HH be the foot of the altitude dropped from the vertex CC. If the distance from the point HH to the side BCBC is equal to the length of the segment HAHA, prove that ∠BDC=18\angle BDC = 18.
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