In a circle, a diameter AB and a chord PQ (which is not a diameter) intersect each other X perpendicularly. If AX : BX = 3 : 2 and the radius of the circle is 5 cm, then the length of chord PQ is

Answer: Option C

AB = 5 unit
AO = 2.5
OP = 2.5
OX = OB - BX
= 2.5 - 2
= 0.5
OP = 2.5 unit
2.5 → 5
1 → 2
0.5 → 0.5 × 2 = 1
In ΔOPX

$$\begin{array}{rl}& \text{PX}=\sqrt{25-1}=\sqrt{24}=2\sqrt{6}\\ & \text{PQ}=2\text{PX}=2\times 2\sqrt{6}=4\sqrt{6}\end{array}$$