Question

find the radius of the circle inscribed in a triangle whose sides are 15cm, 17 cm and 8cm?

Answer 1

make a diagram
Triangle ABC with AB=17, BC=8 and AC = 15

Did you realize that your triangle is right-angled, with angle C = 90° ?

let the points of contact of the circle be
D on BC, E on AC, and F on AB

Two properties we can use ...
1. The centre of the incscribed circle lies on the angle bisectors of the triangle, and
2. BF=BC , AE=AF, and DC = EC, by the tangent properties

let the radius be r,
since the 90° is bisected, DC = r
then BD= 8-r, and of course by #2 BF=8-r
then AF= 9+r and AE = 15-r

I see two similar triangles at the top, so

r/(9+r) = r/(15-r)

solve for r

Answer 2

3cm