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Nice,but easy

Source: Problem 5 from ZIMO 2008

January 21, 2008
symmetrygeometrycircumcircletrigonometrycyclic quadrilateralgeometry proposed

Problem Statement

Let A1A2 A_1A_2 be the external tangent line to the nonintersecting cirlces ω1(O1) \omega_1(O_1) and ω2(O2) \omega_2(O_2),A1∈ω1 A_1\in\omega_1,A2∈ω2 A_2\in\omega_2.Points K K is the midpoint of A1A2 A_1A_2.And KB1 KB_1 and KB2 KB_2 are tangent lines to ω1 \omega_1 and ω2 \omega_2,respectvely(B1≠A1 B_1\neq A_1,B2≠A2 B_2\neq A_2).Lines A1B1 A_1B_1 and A2B2 A_2B_2 meet in point L L,and lines KL KL and O1O2 O_1O_2 meet in point P P. Prove that points B1,B2,P B_1,B_2,P and L L are concyclic.
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