A triangle has corners at $(2 , 9 )$ , $(3 ,7 )$ , and $(1 ,1 )$ . What is the radius of the triangle's inscribed circle?

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Answer 1 · 2016-03-10T08:27:24

$r=0.60158" "$ units

From the given data:
Let A(2, 9) and B(3,7) and C(1,1)

We let side a the distance B to C
We let side b the distance A to C
We let side c the distance A to B

Compute the lengths of the sides

$a=sqrt((x_b-x_c)^2+(y_b-y_c)^2)$
$a=sqrt((3-1)^2+(7-1)^2)$
$a=2sqrt10$

$b=sqrt((x_a-x_c)^2+(y_a-y_c)^2)$
$b=sqrt((2-1)^2+(9-1)^2)$
$b=sqrt(65)$

$c=sqrt((x_a-x_b)^2+(y_a-y_b)^2)$
$c=sqrt((2-3)^2+(9-7)^2)$
$c=sqrt((1+4)$
$c=sqrt5$

We are now ready to compute for the radius $r$ of the triangle's inscribed circle:

Formula $r=sqrt(((s-a)(s-b)(s-c))/s)" " "$ where $s=(a+b+c)/2$

$s=(2sqrt10+sqrt65+sqrt5)/2=8.3114405230675$

$r=$
$sqrt(((8.311440-2sqrt10)(8.311440-sqrt65)(8.311440-sqrt5))/8.311440)$

$r=0.60158" "$ units

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

A triangle has corners at (2 , 9 )(2 , 9 ), (3 ,7 )(3 ,7 ), and (1 ,1 )(1 ,1 ). What is the radius of the triangle's inscribed circle?