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A Cyclic Quadrilateral

Source: Spring 2006 Tournament of Towns Senior O-Level #4

September 9, 2015
geometrycyclic quadrilateral

Problem Statement

Quadrilateral ABCDABCD is a cyclic, AB=ADAB = AD. Points MM and NN are chosen on sides BCBC and CDCD respectfully so that ∠MAN=1/2(∠BAD)\angle MAN =1/2 (\angle BAD). Prove that MN=BM+NDMN = BM + ND.
(5 points)
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