Determine the circle radius if the circle is inscribed in a

Determine the circle radius if the circle is inscribed in a triangle wich has the sides lenghts of 13, 14, and 15.

Solution

We have to find the radius of the circle inscribed in a triangle with sides of length 13, 14 and 15.

Now we have the area of a triangle given as sqrt [ s ( s-a) (s-b) (s-c)] and it is also equal to r*s where s is the semi perimeter and r is the radius of the inscribed circle.

So r*s = sqrt [ s ( s-a) (s-b) (s-c)]

r = sqrt [ s ( s-a) (s-b) (s-c)] / s = sqrt [( s-a) (s-b) (s-c)]/ s ].

As the sides are 13, 14 and 15, the semi perimeter s = 21 .

So substituting we get r = sqrt [ 8* 7* 6 / 21] = sqrt 16 = 4.

So the required radius is 4