In a circle with centre O and radius 13 cm, two parallel chords AB and CD are drawn on opposite sides of the centre. If AB = 10 cm and CD = 24 cm, find the distance between the two chords (in cm).

Solution

Solution: The perpendicular from the centre bisects each chord. For chord AB, half its length is 5 cm, so its distance from the centre is \(\sqrt{13^2-5^2}=\sqrt{144}=12\) cm. For chord CD, half its length is 12 cm, so its distance from the centre is \(\sqrt{13^2-12^2}=\sqrt{25}=5\) cm. Since the chords are on opposite sides of the centre, the distance between them \(=12+5=17\) cm. Trick: Find each chord's distance from the centre using the half-chord and Pythagoras, then add the distances.