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Source: China TST 2023 Problem 16

March 29, 2023
geometry

Problem Statement

Let Γ,Γ1,Γ2\Gamma, \Gamma_1, \Gamma_2 be mutually tangent circles. The three circles are also tangent to a line ll. Let Γ,Γ1\Gamma, \Gamma_1 be tangent to each other at B1B_1, Γ,Γ2\Gamma, \Gamma_2 be tangent to each other at B2B_2, Γ1,Γ2\Gamma_1, \Gamma_2 be tangent to each other at CC. Γ,Γ1,Γ2\Gamma, \Gamma_1, \Gamma_2 are tangent to ll at A,A1,A2A, A_1, A_2 respectively, where AA is between A1,A2A_1,A_2. Let D1=A1C∩A2B2,D2=A2C∩A1B1D_1 = A_1C \cap A_2B_2, D_2 = A_2C \cap A_1B_1. Prove that D1D2D_1D_2 is parallel to ll.
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