A sphere
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Surface of a sphere
With the distance formula. Call the points A, B, and C. Call the sides ab, bc, and ca. If we know where points A and B are, we can figure out the location of point C. We use two distance formulas. The length of cb and the location of B will give us a set of points an equal distance from point B (a circle with center at B). The length of ca and the location of A will give us a set of points an equal distance from point A (a circle with center at A). The intersection of these two sets (set the distance formulas equal to each other, or otherwise solve for the solution of a set of equations) will be the two possibilities of the vertex C.
It is the radius of a circle or of a sphere
The point that is equal distance from the endpoints of a line segment is the midpoint.
The centre of a circle is equal distance from all points of its circumference