We are given
length of sides are
AB=7
AC=7
BC=6
now, we can use formula of area of triangle
[tex] A=r*s [/tex]
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
[tex] s=\frac{a+b+c}{2} [/tex]
a , b and c are values of sides
[tex] s=\frac{7+7+6}{2} [/tex]
[tex] s=10 [/tex]
[tex] A=\sqrt{s(s-a)(s-b)(s-c)} [/tex]
now, we can plug values
[tex] A=\sqrt{10(10-7)(10-7)(10-6)} [/tex]
[tex] A=6\sqrt{10} [/tex]
step-2: Finding radius(r)
we got
[tex] A=6\sqrt{10} [/tex]
[tex] s=10 [/tex]
now, we can find radius
[tex] A=r*s [/tex]
[tex] 6\sqrt{10} =r*10 [/tex]
[tex] r=\frac{3\sqrt{10}}{5} [/tex]............Answer
