Question

AB and CD are two parallel chords of a circle such that AB = 24 cm and CD = 10 cm. If the
radius of the circle is 13 cm. find the distance between the two chords.

Answer 1

Join OA and OC.

Since the perpendicular from the centre of the circle to a chord bisects the chord.

Therefore, N and M are the mid-points of AB and CD respectively.

Consequently

`AN = NB = 1/2 AB = 1/2 xx 24 = 12` cm and

`CM = MD = 1/2 CD = 1/2 xx 10` = 5 cm

In right-angled triangles ANO and CMO, we have

OA²  = ON² + AN² and OC² = OM² + CM²

⇒ 13² = ON² + 12²  and 13² = OM² + 5²

⇒ ON² = 13² - 12² and OM² = 13² - 5²

⇒ ON² = 169 - 144  and OM² = 169 - 25

⇒ ON² = 25  and OM² = 144

⇒ ON = 5 and OM = 12

Now, NM = ON + OM = 5 + 12 = 17cm

Hence, the distance between the two chords is 17 cm.