MathLabs

Problem 2

In a circle CC with centre OO and radius rr, let C1,C2C_1,C_2 have centres O1,O2O_1,O_2 and radii r1,r2r_1,r_2. Each CiC_i is internally tangent to CC at AiA_i, and C1,C2C_1,C_2 are externally tangent at AA. Prove that the lines OAOA, O1A2O_1A_2, and O2A1O_2A_1 are concurrent.
Step 4 of 4: Conclude the required concurrency
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∴OA, O1A2, O2A1 are concurrent\therefore\quad OA,\ O_1A_2,\ O_2A_1\text{ are concurrent}
Detailed analysis

Ceva's theorem proves that the three lines named in the problem have one common point, completing the proof.