A triangle has corners at $(4, 3)$ $(4 ,3 )$ , $(2, 2)$ $(2 ,2 )$ , and $(7, 8)$ $(7 ,8 )$ . What is the radius of the triangle's inscribed circle?

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Answer 1 · 2017-07-08T11:22:50

The radius of the incircle is $= 0.44 u$ $=0.44u$

The area of the triangle is

$A=1/2|(x_1,y_1,1),(x_2,y_2,1),(x_3,y_3,1)|$

$=1/2(x_1(y_2-y_3)-y_1(x_2-x_3)+(x_2y_3-x_3y_2))$

$A=1/2|(4,3,1),(2,2,1),(7,8,1)|$

$=1/2(4*|(2,1),(8,1)|-3*|(2,1),(7,1)|+1*|(2,2),(7,8)|)$

$=1/2(4(2-8)-3(2-7)+1(16-14))$

$=1/2(-24+15+2)$

$=1/2|-7|=7/2$

The length of the sides of the triangle are

$a=sqrt((4-2)^2+(3-2)^2)=sqrt5$

$b=sqrt((7-2)^2+(8-2)^2)=sqrt61$

$c=sqrt((7-4)^2+(8-3)^2)=sqrt34$

Let the radius of the incircle be $=r$

Then,

The area of the circle is

$A=1/2r(a+b+c)$

The radius of the incircle is

$r=(2a)/(a+b+c)$

$=(7)/(sqrt5+sqrt61+sqrt34)$

$=7/15.88=0.44$

A triangle has corners at (4 ,3 )(4,3)(4 ,3 ), (2 ,2 )(2,2)(2 ,2 ), and (7 ,8 )(7,8)(7 ,8 ). What is the radius of the triangle's inscribed circle?