Question

A triangle has corners at `(3 , 3 )`, `(4 ,2 )`, and `(8 ,9 )`. What is the radius of the triangle's inscribed circle?

Answer 1

`r=0.6363265774`

Explanation:

there is a formula for solving the radius r of the inscribed circle

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

where `s=`half the perimeter of the triangle

and `s=1/2*(a+b+c)`

Let `A(3, 3), B(4, 2), C(8, 9)`

so that
`a=`distance from B to C
`b=`distance from A to C
`c=`distance from A to B

`a=sqrt((x_B-x_C)^2+(y_B-y_C)^2)`
`a=sqrt((4-8)^2+(2-9)^2)`
`a=sqrt(16+49)`
`a=sqrt(65)`

`b=sqrt((x_A-x_C)^2+(y_A-y_C)^2)`
`b=sqrt((3-8)^2+(3-9)^2)`
`b=sqrt(25+36)`
`b=sqrt(61)`

`c=sqrt((3-4)^2+(3-2)^2)`
`c=sqrt(1+1)`
`c=sqrt(2)`

Compute `s`

`s=1/2*(a+b+c)`
`s=1/2*(sqrt(65)+sqrt(61)+sqrt(2))`

Compute r

`r = sqrt(((1/2*(sqrt(65)+sqrt(61)+sqrt(2))-sqrt(65))(1/2*(sqrt(65)+sqrt(61)+sqrt(2))-sqrt(61))(1/2*(sqrt(65)+sqrt(61)+sqrt(2))-sqrt(2)))/(1/2*(sqrt(65)+sqrt(61)+sqrt(2))))" "`

`r=sqrt(((0.581102745)(0.8331108174)(7.229146931))/8.643360493)`

`r=0.6363265774`

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