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<AMD = <CMD if tangents at B,D of cyclic ABCD concurrent with AC

Source: Indonesia INAMO Shortlist 2008 G5

August 25, 2021
geometryequal anglescyclic quadrilateral

Problem Statement

Let ABCDABCD be quadrilateral inscribed in a circle. Let MM be the midpoint of the segment BDBD. If the tangents of the circle at B B, and at DD are also concurrent with the extension of ACAC, prove that ∠AMD=∠CMD\angle AMD = \angle CMD.
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