A triangle has corners at $(3 , 4 )$ , $(8 ,2 )$ , and $(5 ,8 )$ . What is the radius of the triangle's inscribed circle?

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Answer 1 · 2018-03-02T13:52:59

Area of the radius of the circumscribed circle is $R = color (purple)( 3.4$ units

Steps :
1. Find the lengths of the three sides using distance formula
$d = sqrt((x2 - x1)^2 + (y2 - y1)^2)$

Find the area of the triangle using formula
$A_t = sqrt(s (s - a) (s - b) ( s - c))$

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$a = sqrt((8-5)^2 + (2-8)^2) ~~ 6.7$

$b = sqrt((5-3)^2 + (8-4)^2) = 5$

$c = sqrt ((3-8)^2 + (4-2)^2) ~~ 5.4$

$s = (a + b + c)/2 = (6.7+5+5.4)/2 = 8.55$

$A_t = sqrt(8.55 * (8.55-6.7) * (8.55-5) * (8.55-5.4)) ~~ 13.3$

$R = (6.7*5*5.4) / (4 * 13.3) = color(purple)(3.4$

A triangle has corners at (3 , 4 )(3 , 4 ), (8 ,2 )(8 ,2 ), and (5 ,8 )(5 ,8 ). What is the radius of the triangle's inscribed circle?