MathDB

8

Part of 2003 Switzerland Team Selection Test

Problems(1)

7 circles related problem, in pairs externally tangent

Source: Switzerland - Swiss TST 2003 p8

2/18/2020
Let A1A2A3A_1A_2A_3 be a triangle and ω1\omega_1 be a circle passing through A1A_1 and A2A_2. Suppose that there are circles ω2,...,ω7\omega_2,...,\omega_7 such that: (a) ωk\omega_k passes through AkA_k and Ak+1A_{k+1} for k=2,3,...,7k = 2,3,...,7, where Ai=Ai+3A_i = A_{i+3}, (b) ωk\omega_k and ωk+1\omega_{k+1} are externally tangent for k=1,2,...,6k = 1,2,...,6. Prove that ω1=ω7\omega_1 = \omega_7.
tangent circlescirclesgeometry