In a circle with centre O, AB and CD are parallel chords on the opposite sides of a diameter. If AB = 12 cm, CD = 18 cm and the distance between the chords AB and CD is 15 cm, then find the radius of the circle (in cm).

From triangle AJO,

r$$^2$$ = 6$$^2$$ + (15 - x)$$^2$$

r$$^2$$ = 36 + (15 - x)$$^2$$..................(1)

From triangle CKO,

r$$^2$$ = 9$$^2$$ + x$$^2$$

r$$^2$$ = 81 + x$$^2$$..................(2)

From (1) and (2),

36 + (15 - x)$$^2$$ = 81 + x$$^2$$

225 + x$$^2$$ - 30x = 45 + x$$^2$$

30x = 180

x = 6

From (2),

r$$^2$$ = 81 + x$$^2$$

r$$^2$$ = 81 + 6$$^2$$

r$$^2$$ = 81 + 36

r$$^2$$ = 137

r = $$3\sqrt{13}$$

Hence, the correct answer is Option C