Two circles of radii 20 cm and 13 cm intersect, and their common chord is 24 cm long. The centres lie on opposite sides of the common chord. How far apart are the centres?

Explanation

1. 01

   The line joining the centres is the perpendicular bisector of the common chord, so half the chord = 12 cm.

2. 02

   Distance of the first centre from the chord = $\sqrt{20^2 - 12^2} = 16$ cm.

3. 03

   Distance of the second centre from the chord = $\sqrt{13^2 - 12^2} = 5$ cm.

4. 04

   Centres on opposite sides: $16 + 5 = 21$ cm.