An isosceles triangle has sides 10 cm, 10 cm and 12 cm. What is the radius of its inscribed circle?

The altitude to the base of 12 splits it into 6 and 6, so its height = √$(100-36)=8$ and the area = ½ × $12\times 8=48{\text{cm}}^2$. The semi-perimeter $s=(10+10+12)/2=16$. Since area = $r\times s,r=48/16=3$ cm.