A triangle has corners at (7 , 9 ), (3 ,7 ), and (1 ,8 ). What is the radius of the triangle's inscribed circle?

1 Answer
Mar 2, 2018

Radius of inscribed circle r_i = A_t / s = 44.72 / 6.4 = color(purple)(6.99

Explanation:

Steps :
1. Find the lengths of the three sides using distance formula
d = sqrt((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))

enter image source here

  1. Find the semi perimeter of the triangle

s = (a + b + c) / 2

  1. Find the area of circum radius using formula
    r_i = A_t / s

enter image source here

a = sqrt((3-1)^2 + (7-8)^2) = 2.24

b = sqrt((7-1)^2 + (9-8)^2) = 6.08

c = sqrt((7-3)^2 + (9-7)^2) = 4.47

s = (2.24 + 6.08 + 4.47) / 2 = 6.4

A_t = sqrt(6.4 * (6.4-2.24) ( 6.4 - 6.08) (6.4 - 4.47)) = 44.72

r_i = A_t / s = 44.72 / 6.4 = color(purple)(6.99