How to find radius of circumscribed circle

A circle is considered circumscribed about a polygon into if it covers all its vertices. Remarkably, the center of this circle coincides with the point of intersection of the perpendiculars drawn from the midpoints of the sides of the polygon. The radius of the described circle depends entirely on the polygon around which it is described.

You will need

• Know of sides of the polygon, its area/perimeter.

Instruction

1. The calculation of the radius of the circumscribed around the triangle of the circle.
   If a circle circumscribed around the triangle with sides a, b, c, area S and angle ?, lying up against the side a, the radius R can be calculated by the following formulas:
   1) R = (a*b*c)/4S;
   2) R = a/2sin?.
2. The calculation of the radius of a circlecircumscribed around a regular polygon.
   To calculate the radius of a circlecircumscribed around a regular polygon, you need to use the following formula:
   R = a/(2 x sin (360 / (2 x n))) where
   a - side of a regular polygon;
   n is the number of sides.