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Equality for acute triangle, and tangents of circumcircle

Source: Problem 6 of Russian Regional Olympiad 2011, grade 11

September 1, 2011
geometrycircumcircleperpendicular bisectorgeometry proposed

Problem Statement

ω\omega is the circumcirle of an acute triangle ABCABC. The tangent line passing through AA intersects the tangent lines passing through points BB and CC at points KK and LL, respectively. The line parallel to ABAB through KK and the line parallel to ACAC through LL intersect at point PP. Prove that BP=CPBP=CP. (Author: P. Kozhevnikov)
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