A triangle has corners at $(3, 5)$ $(3 , 5 )$ , $(4, 7)$ $(4 ,7 )$ , and $(8, 6)$ $(8 ,6 )$ . What is the radius of the triangle's inscribed circle?

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A triangle has corners at $(3, 5)$ $(3 , 5 )$ , $(4, 7)$ $(4 ,7 )$ , and $(8, 6)$ $(8 ,6 )$ . What is the radius of the triangle's inscribed circle?

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Answer 1 · 2017-10-09T18:30:36

Coordinates of incenter are (4.42, 6.09)

Explanation:

Let BC = a, AB = c, CA = b & Perimeter = p;
Let the incenter point be O.
$a = \sqrt{{(3 - 4)}^{2} + {(5 - 7)}^{2}} = \sqrt{5} = 2.236$ $a=sqrt((3-4)^2+(5-7)^2)=sqrt5=2.236$
$b = \sqrt{{(8 - 4)}^{2} + {(6 - 7)}^{2}} = \sqrt{17} = 4.123$ $b=sqrt((8-4)^2+(6-7)^2)=sqrt17=4.123$
$c = \sqrt{{(8 - 3)}^{2} + {(6 - 5)}^{2}} = \sqrt{26} = 5.099$ $c=sqrt((8-3)^2+(6-5)^2)=sqrt26=5.099$

$p = \sqrt{5} + \sqrt{17} + \sqrt{26} = 2.236 + 4.123 + 5.099 = 11.458$ $p=sqrt5+sqrt17+sqrt26=2.236+4.123+5.099=11.458$

$O x = \frac{a A x + b B x + c C x}{p}$ $Ox=(aAx+bBx+cCx)/p$
$O x = \frac{(2.236 \cdot 8) + (4.123 \cdot 3) + (5.099 \cdot 4)}{11.458}$ $Ox=((2.236*8)+(4.123*3)+(5.099*4))/11.458$
$O x = \frac{17.888 + 12.369 + 20.396}{11.458} =$ $Ox=(17.888+12.369+20.396)/11.458=$ 4.421

$O y = \frac{a A y + b B y + c C y}{p}$ $Oy=(aAy+bBy+cCy)/p$
$O y = \frac{(2.236 \cdot 6) + (4.123 \cdot 5) + (5.099 \cdot 7)}{11.458}$ $Oy=((2.236*6)+(4.123*5)+(5.099*7))/11.458$
$O y = \frac{13.416 + 20.615 + 35.693}{11.458} =$ $Oy=(13.416+20.615+35.693)/11.458=$ 6.085
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A triangle has corners at $(3, 5)$ $(3 , 5 )$ , $(4, 7)$ $(4 ,7 )$ , and $(8, 6)$ $(8 ,6 )$ . What is the radius of the triangle's inscribed circle?

1 Answer

Explanation:

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A triangle has corners at (3,5)(3 , 5 ), (4,7)(4 ,7 ), and (8,6)(8 ,6 ). What is the radius of the triangle's inscribed circle?

1 Answer

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A triangle has corners at $(3, 5)$ $(3 , 5 )$ , $(4, 7)$ $(4 ,7 )$ , and $(8, 6)$ $(8 ,6 )$ . What is the radius of the triangle's inscribed circle?