Two parallel chords of lengths 30 cm and 16cm are drawn on the opposite sides of the center of a circle of radius 17 cm. Find the distance between the chords.

Question

Philoid · Accepted Answer

Let radius OA = OC = 17 cm

Chord AB = 30 cm and CD = 16 cm

Draw OL and OM

Therefore,

AP = (1/2) AB

⇒ AP = (1/2) 30 = 15 cm

CQ = (1/2) CD

⇒ CQ = (1/2) 16 = 8 cm

In triangle OAP,

OP² = OA² - AP²

⇒ OP² = 17² - 15²

⇒ OP²= 289 - 225

⇒ OP²= 64

⇒ OP = 8 cm

In triangle OQD,

OQ² = OC² - CQ²

⇒ OQ² = 17² - 8²

⇒ OQ²= 289 - 64

⇒ OQ²= 225

⇒ OQ = 15 cm

Now,

PQ = OP + OQ = 8 + 15 = 23

Hence, distance between chords = 23 cm.