Two circles of radii 10 cm and 17 cm intersect, and their common chord is 16 cm long. The two centres lie on opposite sides of the common chord. What is the distance between the centres?

Half the chord is 8 cm. The distance from the first centre to the chord is √(100 − 64) = 6 cm, and from the second centre it is √(289 − 64) = 15 cm. Because the centres are on opposite sides of the chord, the distance between them is 6 + 15 = 21 cm. (If they were on the same side it would be 15 − 6 = 9 cm.)