Two parallel chords on the same side of the centre of a circle are 12 cm and 20 cm long and the radius of the circle is $$5\sqrt{13}$$ cm. What is the distance (in cm) between the chords?

Length of chord RS = 12 cm

Length of chord PQ = 20cm

Radius = $$5\sqrt{13}$$ cm

Length of US = RS/2 = 12/2 = 6 cm

Length of TQ = PQ/2 = 20/2 = 10 cm

($$\because$$ radius divides the chords in 2 equal parts )

In triangle OUS - 

using the pythagorean theorem-

$$OS^2 = OU^2 + US^2$$

$$(5\sqrt{13})^2 = OU^2 + 6^2$$

$$OU^2$$ = 325 - 36 = 289

OU = $$\sqrt{289}$$ = 17 cm

In triangle OTQ -

Using the pythagorean theorem-

$$OQ^2 = OT^2 + TQ^2$$

$$(5\sqrt{13})^2 = OT^2 + 10^2$$

$$OT^2$$ = 325 - 100 = 225

OT = $$\sqrt{325}$$ = 15 cm

Distance between Chords = OU - OT = 17 - 15 = 2cm