Two chords AB and CD of lengths 4 cm and 10 cm respectively are parallel and are on the same side of the centre O of a circle. If the distance between chords is 3 cm, then what is the diameter of the circle?
Answer & explanation
Correct answer: option 2
Let OP = x cm
In ΔBQO:
(BO)2 = (BQ)2 + (QO)2 = (2)2 + (3 + x)2
In ΔCPO:
(CO)2 = (CP)2 + (PO)2 = (5)2 + (x)2
Hypotenuse of ΔBQO and ΔCPO are same = radius
Therefore,
⇒ (2)2 + (3 + x)2 = (5)2 + (x)2
⇒ 4 + 9 + x2 + 6x = 25 + x2
⇒ 6x = 12
⇒ x = 2
(CO)2 = (CP)2 + (PO)2 = (5)2 + (2)2 = 25 + 4 = 29
OC = \(\sqrt {29}\) = radius
diameter = 2 × OC = 2\(\sqrt {29}\)cm