A triangle has corners at $(4 , 5 )$ , $(3 ,2 )$ , and $(5 ,3 )$ . What is the radius of the triangle's inscribed circle?

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A triangle has corners at $(4 , 5 )$ , $(3 ,2 )$ , and $(5 ,3 )$ . What is the radius of the triangle's inscribed circle?

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Answer 1 · 2016-03-31T01:53:46

The radius $r=0.654929" "$ unit

Explanation:

We use the formula for radius of inscribed circle in a triangle

$r=sqrt(((s-a)(s-b)(s-c))/s)" "$ where a,b,c are the sides of the triangle and $s$ is half of the Perimeter's measure.

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

Using distance formula we compute for the sides

Let side $a$ the distance from $(4, 5)$ to $(3, 2)$
Let side $b$ the distance from $(5, 3)$ to $(3, 2)$
Let side $c$ the distance from $(4, 5)$ to $(5, 3)$

$a=sqrt10$
$b=sqrt5$
$c=sqrt5$

$s=(a+b+c)/2=(sqrt10+sqrt5+sqrt5)/2=(sqrt10+2sqrt5)/2$

Compute $r$

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

$r=sqrt((((sqrt10+2sqrt5)/2-sqrt10)((sqrt10+2sqrt5)/2-sqrt5)((sqrt10+2sqrt5)/2-sqrt5))/((sqrt10+2sqrt5)/2))$

$r=0.654929" "$ unit

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A triangle has corners at $(4 , 5 )$ , $(3 ,2 )$ , and $(5 ,3 )$ . What is the radius of the triangle's inscribed circle?

1 Answer

Explanation:

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Impact of this question

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A triangle has corners at (4 , 5 )(4 , 5 ), (3 ,2 )(3 ,2 ), and (5 ,3 )(5 ,3 ). What is the radius of the triangle's inscribed circle?

1 Answer

Explanation:

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A triangle has corners at $(4 , 5 )$ , $(3 ,2 )$ , and $(5 ,3 )$ . What is the radius of the triangle's inscribed circle?