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concyclic points

Source: Polish MO Second Round 1976 p4

September 8, 2024
geometryConcyclic

Problem Statement

Inside the circle S S there is a circle T T and circles K1,K2,…,Kn K_1, K_2, \ldots, K_n tangent externally to T T and internally to S S , and the circle K1 K_1 is tangent to K2 K_2 , K2 K_2 tangent to K3 K_3 etc. Prove that the points of tangency of the circles K1 K_1 with K2 K_2 , K2 K_2 with K3 K_3 etc. lie on the circle.
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