MathDB
May Olympiad 2012, Level 2, Problem 3

Source:

August 25, 2014
geometryperpendicular bisectorangle bisector

Problem Statement

Let ABCABC be a triangle such that ∠ABC=2∠BCA\angle{ABC} = 2\angle{BCA} and ∠CAB>90∘\angle{CAB}>90^\circ. Let MM be the midpoint of BCBC. The line perpendicular to ACAC that passes through CC cuts the line ABAB at point DD. Show that ∠AMB=∠DMC\angle{AMB} = \angle{DMC}.
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