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Opposite ray of EC such that angle BME equals angle ECA

Source: Vietnam MO 2008, Problem 2

August 26, 2008
trigonometrygeometry unsolvedgeometry

Problem Statement

Given a triangle with acute angle ∠BEC, \angle BEC, let E E be the midpoint of AB. AB. Point M M is chosen on the opposite ray of EC EC such that \angle BME \equal{} \angle ECA. Denote by θ \theta the measure of angle ∠BEC. \angle BEC. Evaluate MCAB \frac{MC}{AB} in terms of θ. \theta.
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