= Circumcircle
= Circumscribed circle of a triangle
{synonym}
The <circumcircle> of a nondegenerate <triangle> is the unique <circle> through its three vertices. Its center is the <circumcenter>, found by intersecting two <perpendicular bisectors>; equality of distances to all three vertices proves existence, and subtracting the squared-distance equations proves uniqueness. For a <right triangle>, the midpoint of its hypotenuse is equidistant from all vertices, so its circumradius is half the hypotenuse length.
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