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Malaysia IMONST 2 Senior Problem 4

Source: Malaysia IMO national selection test 2020

October 19, 2020
geometrytangent circles

Problem Statement

Given are four circles Γ1,Γ2,Γ3,Γ4\Gamma_1, \Gamma_2, \Gamma_3, \Gamma_4. Circles Γ1\Gamma_1 and Γ2\Gamma_2 are externally tangent at point AA. Circles Γ2\Gamma_2 and Γ3\Gamma_3 are externally tangent at point BB. Circles Γ3\Gamma_3 and Γ4\Gamma_4 are externally tangent at point CC. Circles Γ4\Gamma_4 and Γ1\Gamma_1 are externally tangent at point DD. Prove that ABCDABCD is cyclic.
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