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Geometry Mathley 3.4 tangent circles wanted

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June 7, 2020
tangent circlescircumcirclecirclesgeometry

Problem Statement

A triangle ABCABC is inscribed in the circle (O,R)(O,R). A circle (O′,R′)(O',R') is internally tangent to (O)(O) at II such that R<R′R < R'. PP is a point on the circle (O)(O). Rays PA,PB,PCPA, PB, PC meet (O′)(O') at A1,B1,C1A_1,B_1,C_1. Let A2B2C2A_2B_2C_2 be the triangle formed by the intersections of the line symmetric to B1C1B_1C_1 about BCBC, the line symmetric to C1A1C_1A_1 about CACA and the line symmetric to A1B1A_1B_1 about ABAB. Prove that the circumcircle of A2B2C2A_2B_2C_2 is tangent to (O)(O).
Nguyễn Văn Linh
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