In a circle, a diameter AB and a chord PQ (which is not a diameter) intersect each other at X perpendicularly. If AX : BX = 3 : 2 and the radius of the circle is 5 cm, then the length of chord PQ is:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 4√6 cm
Let OX = a
BX = 5 - a
AX = 5 + a
Now,
AX/BX = 3/2
⇒ (5 + a)/(5 - a) = 3/2
⇒ 10 + 2a = 15 - 3a
⇒ 5a = 5
⇒ a = 1 cm
Hence,
BX = 4 and AX = 6
In triangle PXO:
PX = √[PO2 - OX2] = √[52 - 12] = 2√6 cm
So,
PQ = 2 × PX = 4√6 cm