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Seven circles tangent to another circle and two sides.

Source: ILL 1979-51

June 5, 2011
geometry unsolvedgeometry

Problem Statement

Let ABCABC be an arbitrary triangle and let S1,S2,⋯ ,S7S_1, S_2,\cdots, S_7 be circles satisfying the following conditions: S1S_1 is tangent to CACA and ABAB, S2S_2 is tangent to S1,ABS_1, AB, and BC,BC, S3S_3 is tangent to S2,BCS_2, BC, and CA,CA, .............................. S7S_7 is tangent to S6,CAS_6, CA and AB.AB. Prove that the circles S1S_1 and S7S_7 coincide.
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