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two tangent circles

Source: Russian MO 1994

June 11, 2008
geometryparallelogramgeometry unsolved

Problem Statement

Point P P is taken inside a right angle KLM KLM. A circle S1 S_1 with center O1 O_1 is tangent to the rays LK,LP LK,LP of angle KLP KLP at A,D A,D respectively. A circle S2 S_2 with center O2 O_2 is tangent to the rays of angle MLP MLP, touching LP LP at B B. Suppose A,B,O1 A,B,O_1 are collinear. Let O2D,KL O_2D,KL meet at C C. Prove that BC BC bisects angle ABD ABD.
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