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convex quadrilateral suggesting a trigonometric solution

Source: Third Zhautykov Olympiad, Kazakhstan, 2007

April 25, 2007
trigonometrygeometrygeometric transformationreflectiongeometry proposed

Problem Statement

Let ABCDABCD be a convex quadrilateral, with ∠BAC=∠DAC\angle BAC=\angle DAC and MM a point inside such that ∠MBA=∠MCD\angle MBA=\angle MCD and ∠MBC=∠MDC\angle MBC=\angle MDC. Show that the angle ∠ADC\angle ADC is equal to ∠BMC\angle BMC or ∠AMB\angle AMB.
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