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RMO 2017 P5

Source: RMO 2017 P5

October 8, 2017
geometrycircles

Problem Statement

Let Ω\Omega be a circle with a chord ABAB which is not a diameter. Γ1\Gamma_{1} be a circle on one side of ABAB such that it is tangent to ABAB at CC and internally tangent to Ω\Omega at DD. Likewise, let Γ2\Gamma_{2} be a circle on the other side of ABAB such that it is tangent to ABAB at EE and internally tangent to Ω\Omega at FF. Suppose the line DCDC intersects Ω\Omega at X≠DX \neq D and the line FEFE intersects Ω\Omega at Y≠FY \neq F. Prove that XYXY is a diameter of Ω\Omega .
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