Question

What is the radius of the circle inscribed in triangle $ABC$ if $AB = AC=7, BC=6$? Express your answer in simplest radical form.

Answer 1

We are given

length of sides are

AB=7

AC=7

BC=6

now, we can use formula of area of triangle

`A=r*s`

where

A is area of triangle

r is radius of in-circle

s is semi-perimeter of triangle

step-1: Finding area of triangle

We can use

Heron's formula

`s=(a+b+c)/(2)`

a , b and c are values of sides

`s=(7+7+6)/(2)`

`s=10`

`A=√(s(s-a)(s-b)(s-c))`

now, we can plug values

`A=√(10(10-7)(10-7)(10-6))`

`A=6√(10)`

step-2: Finding radius(r)

we got

`A=6√(10)`

`s=10`

now, we can find radius

`A=r*s`

`6√(10) =r*10`

`r=(3√(10))/(5)`............Answer