MathDB

51

Part of 1979 IMO Longlists

Problems(1)

Seven circles tangent to another circle and two sides.

Source: ILL 1979-51

6/5/2011
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.
geometry unsolvedgeometry