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Geometry Mathley 11.3 DM/DA = AM/AB iff <AMB = 2<ABC

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June 7, 2020
geometryequal anglesanglesequal ratio

Problem Statement

Let ABCABC be a triangle such that AB=ACAB = AC and let MM be a point interior to the triangle. If BMBM meets ACAC at DD. show that DMDA=AMAB\frac{DM}{DA}=\frac{AM}{AB} if and only if ∠AMB=2∠ABC\angle AMB = 2\angle ABC.
Michel Bataille
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