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Prove midpoint

Source: China North MO

August 14, 2006
projective geometrygeometry unsolvedgeometry

Problem Statement

ABAB is the diameter of circle OO, CDCD is a non-diameter chord that is perpendicular to ABAB. Let EE be the midpoint of OCOC, connect AEAE and extend it to meet the circle at point PP. Let DPDP and BCBC meet at FF. Prove that FF is the midpoint of BCBC.
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