MathDB
Six tangent circles

Source: 2017 Korean Winter Program Practice Test 1 Day 1 #1

January 18, 2017
geometrycircles

Problem Statement

Let γ1,γ2,γ3\gamma_1, \gamma_2, \gamma_3 be mutually externally tangent circles and Γ1,Γ2,Γ3\Gamma_1, \Gamma_2, \Gamma_3 also be mutually externally tangent circles. For each 1≤i≤31 \le i \le 3, γi\gamma_i and Γi+1\Gamma_{i+1} are externally tangent at AiA_i, γi\gamma_i and Γi+2\Gamma_{i+2} are externally tangent at BiB_i, and γi\gamma_i and Γi\Gamma_i do not meet. Show that the six points A1,A2,A3,B1,B2,B3A_1, A_2, A_3, B_1, B_2, B_3 lie on either a line or a circle.
Back to ProblemsView on AoPS