AB and CD are two parallel chords drawn in a circle with centre O. The distance between the two chords is 21 cm. If the lengths of AB and CD are 24 cm and 18 cm, respectively, then the radius of the circle is equal to:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 15 cm.
According to the given question,
Let the line joining the two chord cut chord AB and CD at points M and N respectively.
Let OM = x cm, then ON = (21 - x) cm
In triangle OMB, OB2 = BM2 + OM2
⇒ OB2 = 144 + x2
Also, in triangle OND, OD2 = DN2 + ON2
⇒ OD2 = 81 + (21 - x)2
OB = OD = radius
⇒ 144 + x2 = 81 + 441 + x2 - 42x
⇒ 42x = 378
⇒ x = 9
Now, OB2 = 144 + 81
⇒ OB2 = 225
⇒ OB = 15 cm