A triangle has corners at $(3, 3)$ $(3 , 3 )$ , $(4, 2)$ $(4 ,2 )$ , and $(8, 9)$ $(8 ,9 )$ . What is the radius of the triangle's inscribed circle?

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A triangle has corners at $(3, 3)$ $(3 , 3 )$ , $(4, 2)$ $(4 ,2 )$ , and $(8, 9)$ $(8 ,9 )$ . What is the radius of the triangle's inscribed circle?

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Answer 1 · 2016-11-20T04:57:26

$r = 0.6363265774$ $r=0.6363265774$

Explanation:

there is a formula for solving the radius r of the inscribed circle

$r = \sqrt{\frac{(s - a) (s - b) (s - c)}{s}}$ $r = sqrt(((s-a)(s-b)(s-c))/s)" "$

where $s =$ $s=$ half the perimeter of the triangle

and $s = \frac{1}{2} \cdot (a + b + c)$ $s=1/2*(a+b+c)$

Let $A (3, 3), B (4, 2), C (8, 9)$ $A(3, 3), B(4, 2), C(8, 9)$

so that
$a =$ $a=$ distance from B to C
$b =$ $b=$ distance from A to C
$c =$ $c=$ distance from A to B

$a = \sqrt{{(x_{B} - x_{C})}_{B}^{2} + {(y_{B} - y_{C})}_{B}^{2}}$ $a=sqrt((x_B-x_C)^2+(y_B-y_C)^2)$
$a = \sqrt{{(4 - 8)}^{2} + {(2 - 9)}^{2}}$ $a=sqrt((4-8)^2+(2-9)^2)$
$a = \sqrt{16 + 49}$ $a=sqrt(16+49)$
$a = \sqrt{65}$ $a=sqrt(65)$

$b = \sqrt{{(x_{A} - x_{C})}_{A}^{2} + {(y_{A} - y_{C})}_{A}^{2}}$ $b=sqrt((x_A-x_C)^2+(y_A-y_C)^2)$
$b = \sqrt{{(3 - 8)}^{2} + {(3 - 9)}^{2}}$ $b=sqrt((3-8)^2+(3-9)^2)$
$b = \sqrt{25 + 36}$ $b=sqrt(25+36)$
$b = \sqrt{61}$ $b=sqrt(61)$

$c = \sqrt{{(3 - 4)}^{2} + {(3 - 2)}^{2}}$ $c=sqrt((3-4)^2+(3-2)^2)$
$c = \sqrt{1 + 1}$ $c=sqrt(1+1)$
$c = \sqrt{2}$ $c=sqrt(2)$

Compute $s$ $s$

$s = \frac{1}{2} \cdot (a + b + c)$ $s=1/2*(a+b+c)$
$s = \frac{1}{2} \cdot (\sqrt{65} + \sqrt{61} + \sqrt{2})$ $s=1/2*(sqrt(65)+sqrt(61)+sqrt(2))$

Compute r

$r = \sqrt{\frac{(\frac{1}{2} \cdot (\sqrt{65} + \sqrt{61} + \sqrt{2}) - \sqrt{65}) (\frac{1}{2} \cdot (\sqrt{65} + \sqrt{61} + \sqrt{2}) - \sqrt{61}) (\frac{1}{2} \cdot (\sqrt{65} + \sqrt{61} + \sqrt{2}) - \sqrt{2})}{\frac{1}{2} \cdot (\sqrt{65} + \sqrt{61} + \sqrt{2})}}$ $r = sqrt(((1/2*(sqrt(65)+sqrt(61)+sqrt(2))-sqrt(65))(1/2*(sqrt(65)+sqrt(61)+sqrt(2))-sqrt(61))(1/2*(sqrt(65)+sqrt(61)+sqrt(2))-sqrt(2)))/(1/2*(sqrt(65)+sqrt(61)+sqrt(2))))" "$

$r = \sqrt{\frac{(0.581102745) (0.8331108174) (7.229146931)}{8.643360493}}$ $r=sqrt(((0.581102745)(0.8331108174)(7.229146931))/8.643360493)$

$r = 0.6363265774$ $r=0.6363265774$

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

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A triangle has corners at $(3, 3)$ $(3 , 3 )$ , $(4, 2)$ $(4 ,2 )$ , and $(8, 9)$ $(8 ,9 )$ . What is the radius of the triangle's inscribed circle?

1 Answer

Explanation:

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A triangle has corners at (3,3)(3 , 3 ), (4,2)(4 ,2 ), and (8,9)(8 ,9 ). What is the radius of the triangle's inscribed circle?

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A triangle has corners at $(3, 3)$ $(3 , 3 )$ , $(4, 2)$ $(4 ,2 )$ , and $(8, 9)$ $(8 ,9 )$ . What is the radius of the triangle's inscribed circle?