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Circles and tangents

Source: Moldova NMO 2002 grade 9 problem nr.8

November 3, 2008
geometrygeometric transformationreflectionsymmetry

Problem Statement

The circles C1 C_1 and C2 C_2 with centers O1 O_1 and O2 O_2 respectively are externally tangent. Their common tangent not intersecting the segment O1O2 O_1O_2 touches C1 C_1 at A A and C2 C_2 at B B. Let C C be the reflection of A A in O1O2 O_1O_2 and P P be the intersection of AC AC and O1O2 O_1O_2. Line BP BP meets C2 C_2 again at L L. Prove that line CL CL is tangent to the circle C2 C_2.
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