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Moldova mo 2006, 10th grade

Source: Moldova MO 2006

March 21, 2006
geometrytrapezoidgeometry unsolved

Problem Statement

A convex quadrilateral ABCD ABCD is inscribed in a circle. The tangents to the circle through A A and C C intersect at a point P P, such that this point P P does not lie on BD BD, and such that PA2=PBā‹…PD PA^{2}=PB\cdot PD. Prove that the line BD BD passes through the midpoint of AC AC.
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