Derivation of Formula for the Radius of Incircle

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 inscribed circle (incircle) given the value of the area and the three sides, simply divide the area by the half of the perimeter (s). In other words, the radius of the incircle is the ratio of the Area of the triangle to its half of the Perimeter.

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

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

The Formula

where A = area of the triangle and s = ½ (a + b + c).

Derivation of the radius of Incircle

Finally,

where A = area of the triangle and s = ½ (a + b + c).

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