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if MA\cdot MC + MA\cdot CD = MB \cdot MD then <BKC =< BDC

Source: Slovenia TST 2005 p1

February 15, 2020
equal anglesgeometrydiagonals

Problem Statement

The diagonals of a convex quadrilateral ABCDABCD intersect at MM. The bisector of ∠ACD\angle ACD intersects the ray BABA at KK. Prove that if MA⋅MC+MA⋅CD=MB⋅MDMA\cdot MC + MA\cdot CD = MB \cdot MD , then ∠BKC=∠BDC\angle BKC = \angle BDC
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