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Trangles with same circumradius

Source: 10.8 of XX Geometrical Olympiad in honour of I.F.Sharygin

August 7, 2024
geogeometrycircumcircle

Problem Statement

The common tangents to the circumcircle and an excircle of triangle ABCABC meet BC,CA,ABBC, CA,AB at points A1,B1,C1A_1, B_1, C_1 and A2,B2,C2A_2, B_2, C_2 respectively. The triangle Δ1\Delta_1 is formed by the lines AA1,BB1AA_1, BB_1, and CC1CC_1, the triangle Δ2\Delta_2 is formed by the lines AA2,BB2,AA_2, BB_2, and CC2CC_2. Prove that the circumradii of these triangles are equal.
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