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Paraguayan National Olympiad 2008, Level 3, Problem 4

Source:

August 31, 2014
geometryincenterAsymptote

Problem Statement

Let Γ\Gamma be a circumference and AA a point outside it. Let BB and CC be points in Γ\Gamma such that ABAB and ACAC are tangent to Γ\Gamma. Let PP be a point in Γ\Gamma. Let DD, EE and FF be points in BCBC, ACAC and ABAB respectively, such that PD⊥BCPD \perp BC, PE⊥ACPE \perp AC, and PF⊥ABPF \perp AB. Show that PD2=PE⋅PFPD^2 = PE \cdot PF
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