A triangle has corners at (3 , 4 )(3,4), (6 ,3 )(6,3), and (5 ,8 )(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√(6−3)2+(3−4)2=√10
sqrt{(6 - 5)^2 + (3 - 8)^2} = sqrt26√(6−5)2+(3−8)2=√26
sqrt{(3 - 5)^2 + (4 - 8)^2} = 3sqrt2√(3−5)2+(4−8)2=3√2
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
