Inscribed Circle

Answer: 1.41 cm

by tangent property, i am sure you know that
a + b = 6
b + c = 5
c + a = 9
add up 3 equations, 2(a + b + c) = 20 => a + b + c = 10
a + (5) = 10 => a = 5
b + (9) = 10 => b = 1
c + (6) = 10 => c = 4

Let r be the 3 radii of the inscribed circle
and A be the angle intesect by 6 cm and 5 cm
by cosine formula, cos A = (6^2 + 5^2 - 9^2) / (2 x 6 x 5) => A = 109.471
so, tan(A / 2) = r / 1 => r = tan(109.471 / 2) = 1.41

thus, the radius is 1.41 cm

Let r cm be the radius of the inscribed circle.
Half of the perimeter of triangle=s=(6+5+9)/2=10.
Then area of the triangle = rs=10r
Also,by Heron's formula,
area of triangle=√ [s(s-6)(s-5)(s-9)]=√ [10(4)(5)(1)]=10√2
Thus 10r=10√2
r=√2=1.41 (3 sig. fig.)