For any triangle, nine significant points, including the midpoints of its sides, the feet of its altitudes, and the midpoints of the segments from each vertex to the orthocenter, all lie on a single circle. A classical result of triangle geometry, sometimes attributed jointly to several nineteenth-century geometers.
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StatementFor any triangle, a single circle passes through nine significant points: the midpoint of each side, the foot of each altitude, and the midpoint of the segment from each vertex to the orthocenter. 1 Classification
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1. Nine-Point Circle Theorem (Wikipedia)
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In geometry, the nine-point circle is a circle that can be constructed for any given triangle. It is so named because it passes through nine significant concyclic points defined from the triangle.
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