In a right-angled triangle, the two sides containing the right angle measure 15 cm and 20 cm. What is the sum of its inradius and circumradius?

Hypotenuse = √(15² + 20²) = √625 = 25 cm.

Circumradius of a right triangle = hypotenuse/2 = 12.5 cm (the hypotenuse is a diameter).

Inradius of a right triangle = (a + b − c)/2 = (15 + 20 − 25)/2 = 5 cm. (Check: area/semi-perimeter = 150/30 = 5 ✓.)

Sum = 12.5 + 5 = 17.5 cm.

Tip: r = (a + b − c)/2 and R = c/2 for right triangles — worth memorising.