Question

A triangle has sides with lengths of 2, 7, and 6. What is the radius of the triangles inscribed circle?

Answer 1

In-circle radius `color(brown)(r = A_t / s ~~ 0.7416` units.

Explanation:

Lengths of sides `a = 2, b = 7, c = 6`

In-circle radius `r = A_t / s`

Semi perimeter of triangle `s = (a + b + c)/2 = (2+7+6)/2 = 7.5` units

Area of triangle `A_t = sqrt(s (s-a) (s-b) (s-c))`, using Heron’s formula.

`A_t = (7.5 (7.5-2) (7.5-7) (7.5-6)) = 5.5621` sq. units

In-circle radius `color(brown)(r = A_t / s = 5.5621 / 7.5 ~~ 0.7416` units.