A triangle has corners at $(2 , 5 )$ , $(4 ,8 )$ , and $(4 ,6 )$ . What is the radius of the triangle's inscribed circle?

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Answer 1 · 2016-08-01T07:08:17

Radius of triangle's inscribed circle is $0.52$

If the sides of a triangle are $a$ , $b$ and $c$ , then the area of the triangle $Delta$ is given by the formula

$Delta=sqrt(s(s-a)(s-b)(s-c))$ , where $s=1/2(a+b+c)$

and radius of inscribed circle is $Delta/s$

Hence let us find the sides of triangle formed by $(2,5)$ , $(4,8)$ and $(4,6)$ . This will be surely distance between pair of points, which is

$a=sqrt((4-2)^2+(8-5)^2)=sqrt(4+9)=sqrt13=3.6056$

$b=sqrt((4-4)^2+(6-8)^2)=sqrt(0+4)=sqrt4=2$ and

$c=sqrt((4-2)^2+(6-5)^2)=sqrt(4+1)=sqrt5=2.2631$

Hence $s=1/2(3.6056+2+2.2631)=1/2xx7.8687=3.9344$

and $Delta=sqrt(3.9344xx(3.9344-3.6056)xx(3.9344-2)xx(3.9344-2.2631)$

= $sqrt(3.9344xx0.3288xx1.9344xx1.6713)=sqrt4.18226=2.045$

And radius of inscribed circle is $2.045/3.9344=0.52$

A triangle has corners at (2 , 5 )(2 , 5 ), (4 ,8 )(4 ,8 ), and (4 ,6 )(4 ,6 ). What is the radius of the triangle's inscribed circle?