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Midpoint Created by Tangents

Source: 2008 Philippine Mathematical Olympiad Problem 3

May 6, 2014
projective geometrygeometrycircumcirclegeometry unsolved

Problem Statement

Let PP be a point outside a circle Γ\Gamma, and let the two tangent lines through PP touch Γ\Gamma at AA and BB. Let CC be on the minor arc ABAB, and let ray PCPC intersect Γ\Gamma again at DD. Let ℓ\ell be the line through BB and parallel to PAPA. ℓ\ell intersects ACAC and ADAD at EE and FF, respectively. Prove that BB is the midpoint of EFEF.
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