A right-angled triangle has sides 8 cm, 15 cm and 17 cm. Find the radius, in cm, of the circle drawn inside it touching all three sides.

Area = ½ × $8\times 15=60{\text{cm}}^2$ and $s=(8+15+17)/2=20$ cm, so the radius of the touching circle = area ÷ $s=60/20=3$ cm. (Half the hypotenuse, 8.5 cm, is the radius of the circle through the three corners — a different circle altogether.)