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?

1 Answer
sankarankalyanam
Mar 2, 2018

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

Explanation:

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

  1. Find the area of the triangle using formula
    A_t = sqrt(s (s - a) (s - b) ( s - c))At=√s(s−a)(s−b)(s−c)

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  1. Find the area of circum radius using formula
    R = (abc) / (4A_t)R=abc4At

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a = sqrt((8-5)^2 + (2-8)^2) ~~ 6.7a=√(8−5)2+(2−8)2≈6.7

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

c = sqrt ((3-8)^2 + (4-2)^2) ~~ 5.4c=√(3−8)2+(4−2)2≈5.4

s = (a + b + c)/2 = (6.7+5+5.4)/2 = 8.55s=a+b+c2=6.7+5+5.42=8.55

A_t = sqrt(8.55 * (8.55-6.7) * (8.55-5) * (8.55-5.4)) ~~ 13.3At=√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)(3.4R=6.7⋅5⋅5.44⋅13.3=3.4

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