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BE = BF wanted, cyclic ABCD

Source: Indonesia INAMO Shortlist 2009 G3 https://artofproblemsolving.com/community/c1101409_

December 11, 2021
geometryequal segmentscyclic quadrilateral

Problem Statement

Given a quadrilateral ABCDABCD inscribed in circle Γ\Gamma.From a point P outside Γ\Gamma, draw tangents PAPA and PBPB with AA and BB as touspoints. The line PCPC intersects Γ\Gamma at point DD. Draw a line through BB parallel to PAPA, this line intersects ACAC and ADAD at points EE and FF respectively. Prove that BE=BFBE = BF.
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