Question

A triangle has corners at `(2 , 6 )`, `(8 ,2 )`, and `(1 ,3 )`. What is the radius of the triangle's inscribed circle?

Answer 1

`color(orange)("Radius of incircle " r = A_t / s = 10.99 / 8.72 = 1.26 " units"`

Explanation:


`"Incircle radius " r = A_t / s`

`A(2,6), B(8,2), C(1,3)`

`a = sqrt((8-1)^2 + (2-3)^2) = 7.07`

`b = sqrt((1-2)^2 + (3-6)^2) = 3.16`

`c = sqrt((2-8)^2 + (6-2)^2) = 7.21`

`"Semi-perimeter " s = (a + b + c) / 2 = (7.07 + 3.16 + 7.21) / 2 = 8.72`

`"A_t = sqrt(s (s-a) s-b) (s-c))`

`A_t = sqrt(8.72 (8.72-7.07) (8.72 - 3.16) (8.72 - 7.21)) = 10.99`

`color(orange)("Radius of incircle " r = A_t / s = 10.99 / 8.72 = 1.26 " units"`