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A line passing through the circumcenter

Source: MEMO 2024 T5

August 27, 2024
geometrycircumcirclegeometry proposed

Problem Statement

Let ABCABC be a triangle with ∠BAC=60∘\angle BAC=60^\circ. Let DD be a point on the line ACAC such that AB=ADAB = AD and AA lies between CC and DD. Suppose that there are two points E≠FE \ne F on the circumcircle of the triangle DBCDBC such that AE=AF=BCAE = AF = BC. Prove that the line EFEF passes through the circumcenter of ABCABC.
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