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2

Part of 2013 IberoAmerican

Problems(1)

Iberoamerican Olympiad 2013 - Problem 2

Source: http://oim2013.opm.org.pa/pdfs/examen_pt.pdf

8/13/2014
Let XX and YY be the diameter's extremes of a circunference Γ\Gamma and NN be the midpoint of one of the arcs XYXY of Γ\Gamma. Let AA and BB be two points on the segment XYXY. The lines NANA and NBNB cuts Γ\Gamma again in CC and DD, respectively. The tangents to Γ\Gamma at CC and at DD meets in PP. Let MM the the intersection point between XYXY and NPNP. Prove that MM is the midpoint of the segment ABAB.
geometrypower of a pointradical axisgeometry proposed