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RMO 2024 Q3

Source: RMO 2024 Q3

November 3, 2024
geometrycircumcircle

Problem Statement

Let ABCABC be an acute triangle with AB=ACAB = AC. Let DD be the point on BCBC such that ADAD is perpendicular to BCBC. Let O,H,GO,H,G be the circumcenter, orthocenter and centroid of triangle ABCABC respectively. Suppose that 2⋅OD=23⋅HD2 \cdot OD = 23 \cdot HD. Prove that GG lies on the incircle of triangle ABCABC.
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