The circles of same radius 13 cm intersect each other at A and B. If AB = 10 cm, then the distance between their centres is :

24 cm

As we can see the radius of the circle = 13

and the distance of AO = 5

So, according to the pythagoras theorem =

AM² = AO² + MO²

(13)² = (5)² + MO²

169 - 25 = MO²

144 = MO²

MO = \(\sqrt {144}\) = 12

So the difference between their centers = MN = 12 × 2 = 24