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11.2

Part of 2004 All-Russian Olympiad Regional Round

Problems(1)

3 equal circles int. tangent to 4th - All-Russian MO 2004 Regional (R4) 11.2

Source:

9/27/2024
Three circles ω1\omega_1, ω2\omega_2, ω3\omega_3 of radius rr pass through the pointS S and internally touch the circle ω\omega of radius RR (R>rR > r) at points T1T_1, T2T_2, T3T_3 respectively. Prove that the line T1T2T_1T_2 passes through the second (different from SS) intersection point of the circles ω1\omega_1 and ω2\omega_2.
geometrytangent circlesequal circles