A triangle has corners at $(3 , 4 )$ , $(8 ,2 )$ , and $(1 ,8 )$ . What is the radius of the triangle's inscribed circle?

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Answer 1 · 2016-05-14T04:59:47

The radius of inscribed circle $r=0.8387131004" "$ unit

Let us label the points $A(3, 4)$ , $B(8, 2)$ , $C(1, 8)$
Solve for the distances $a=BC$ and $b=AC$ and $c=AB$

The radius of the inscribed circle $r$ formula

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

Solve for the values of s, a, b, and c first

$a=sqrt((x_b-x_c)^2+(y_b-y_c)^2)$
$a=sqrt((8-1)^2+(2-8)^2)$
$a=sqrt85$

$b=sqrt((x_a-x_c)^2+(y_a-y_c)^2)$
$b=sqrt((3-1)^2+(4-8)^2)$
$b=sqrt20$

$c=sqrt((x_a-x_b)^2+(y_a-y_b)^2)$
$c=sqrt((3-8)^2+(4-2)^2)$
$c=sqrt(29)$

Half the Perimeter of the triangle $s$

$s=(a+b+c)/2=(sqrt85+sqrt20+sqrt29)/2$

Compute $r$

$r=$
$sqrt((((sqrt85+sqrt20+sqrt29)/2-a)((sqrt85+sqrt20+sqrt29)/2-b)((sqrt85+sqrt20+sqrt29)/2-c))/[0.5*(sqrt85+sqrt20+sqrt29)])$

$r=0.8387131004$

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

A triangle has corners at (3 , 4 )(3 , 4 ), (8 ,2 )(8 ,2 ), and (1 ,8 )(1 ,8 ). What is the radius of the triangle's inscribed circle?