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Triangle geometry, bisecting chords

Source: BWM 2004, 2nd round, problem 3

September 1, 2004
geometryratiosimilar trianglesgeometry proposed

Problem Statement

Given two circles k1k_1 and k2k_2 which intersect at two different points AA and BB. The tangent to the circle k2k_2 at the point AA meets the circle k1k_1 again at the point C1C_1. The tangent to the circle k1k_1 at the point AA meets the circle k2k_2 again at the point C2C_2. Finally, let the line C1C2C_1C_2 meet the circle k1k_1 in a point DD different from C1C_1 and BB. Prove that the line BDBD bisects the chord AC2AC_2.
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