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sum of 3 angles = 180^o, 3 circles - All-Russian MO 1998 Regional (R4) 8.7

Source:

September 17, 2024
geometryangles

Problem Statement

Let OO be the center of a circle circumscribed about an acute angle triangle ABCABC, SAS_A, SBS_B, SCS_C - circles with center O, tangent to sides BCBC, CACA, ABAB respectively. Prove that the sum of three angles : between the tangents to SAS_A drawn from point AA, to SBS_B from point BB and to SCS_C - from point CC, is equal to 180o180^o.
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