Question

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

Answer 1

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

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))`

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

`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`