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Part of 1995 Czech And Slovak Olympiad IIIA

Problems(1)

3 tangent circles, angles chasing

Source: Czech And Slovak Mathematical Olympiad, Round III, Category A 1995 p5

2/20/2020
Let A,BA,B be points on a circle kk with center SS such that ∠ASB=90o\angle ASB = 90^o . Circles k1k_1 and k2k_2 are tangent to each other at ZZ and touch kk at AA and BB respectively. Circle k3k_3 inside ∠ASB\angle ASB is internally tangent to kk at CC and externally tangent to k1k_1 and k2k_2 at XX and YY, respectively. Prove that ∠XCY=45o\angle XCY = 45^o
anglestangent circlesgeometry