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nine-point circle SAM.

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nine-point circle MAT.

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The midpoints of the three sides and the feet of the three altitudes all lie on a single circle, the triangle's nine-point circle. en.wikipedia.org

The triangle's nine-point circle has half the diameter of the circumcircle. en.wikipedia.org

The nine-point circles are all congruent with a radius of half that of the cyclic quadrilateral's circumcircle. en.wikipedia.org

The remaining six intersection points of these nine-point circles each concur with the midpoints of the four triangles. en.wikipedia.org

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