Derivation of Formula for the Radius of Circumcircle

Most of the Plane Geometry problems in triangle could be easy solve by direct substitution using the applicable formula according to the given value of the problems. To find the radius of the circumscribed circle (circumcircle) given the value of the area and the three sides, simply divide the product of the three sides by 4 times the area of the triangle. In other words, the radius of the circumcircle is the ratio of the product of the three sides to 4 times the area.

If you are wondering how we came up with the formula, just follow the derivation below.

• If are looking for the radius of incircle see the derivation of formula for radius of incircle.

The Formula

where R = radius of Circumscribed Circle and a, b and c are the sides.

Derivation of the radius of Circumcircle

Finally,

where R = radius of Circumscribed Circle and a, b and c are the sides.

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