MathDB
Concurrency

Source: APMO 1992

March 11, 2006
trigonometrygeometrygeometry unsolved

Problem Statement

In a circle CC with centre OO and radius rr, let C1C_1, C2C_2 be two circles with centres O1O_1, O2O_2 and radii r1r_1, r2r_2 respectively, so that each circle CiC_i is internally tangent to CC at AiA_i and so that C1C_1, C2C_2 are externally tangent to each other at AA. Prove that the three lines OAOA, O1A2O_1 A_2, and O2A1O_2 A_1 are concurrent.
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