Question

A triangle has corners at `(4 , 5 )`, `(3 ,2 )`, and `(1 ,7 )`. What is the radius of the triangle's inscribed circle?

Answer 1

Radius `r=0.905127" "`units

Explanation:

Using the given corners A(4, 5), B(3, 2), C(1, 7)
compute the sides and they are as follows;
`a=sqrt29`
`b=sqrt13`
`c=sqrt10`
`s=1/2(sqrt29+sqrt13+sqrt10)`
and radius r of inscribed triangle

`r=sqrt(((s-a)(s-b)(s-c))/s)`

`r=0.905127" "`units

God bless...I hope the explanation is useful.