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MD = KD wanted, isosceles, AM = 2DC,<AMD =<KDC (2018 Kyiv City MO Round2 8.3.1)

Source:

September 14, 2020
geometryisoscelesequal anglesequal segments

Problem Statement

On the sides ABAB, BCBC and CACA of the isosceles triangle ABCABC with the vertex at the point BB marked the points MM, DD and KK respectively so that AM=2DCAM = 2DC and ∠AMD=∠KDC\angle AMD = \angle KDC. Prove that MD=KDMD = KD.
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