A triangle has corners at #(3 , 4 )#, #(6 ,3 )#, and #(5 ,8 )#. What is the radius of the triangle's inscribed circle?
1 Answer
Explanation:
First, we find the length of each side of the triangle using the Pythagorean Theorem.
#sqrt{(6 - 3)^2 + (3 - 4)^2} = sqrt10#
#sqrt{(6 - 5)^2 + (3 - 8)^2} = sqrt26#
#sqrt{(3 - 5)^2 + (4 - 8)^2} = 3sqrt2#
There is a short way to find the radius of the incircle. It is given by the following formula.
#"Radius of Incircle" = frac{2 * "Area of "Delta}{"Perimeter of "Delta}#
The perimeter is
The area is found quickly using Heron's Formula.
The semi-perimeter is
The area is
The radius is