A circle is inscribed in an isosceles trapezium whose parallel sides are 8 cm and 18 cm. What is the radius of the circle?

A quadrilateral with an incircle has equal sums of opposite sides, so the two equal legs add to 8 + 18 = 26 cm and each leg is 13 cm. The horizontal offset of a leg is $(18-8)/2=5$ cm, so the height is $\sqrt{13^2-5^2}=12$ cm. The diameter equals the height, so $r=6$ cm.