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

A. $$2\sqrt {13} {\text{ cm}}$$

B. $$5\sqrt 3 {\text{ cm}}$$

C. $$4\sqrt 6 {\text{ cm}}$$

D. $$4\sqrt 5 {\text{ cm}}$$

Answer: Option C

Solution (By Examveda Team)

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

$$\eqalign{ & {\text{PX}} = \sqrt {25 - 1} = \sqrt {24} = 2\sqrt 6 \cr & {\text{PQ}} = 2{\text{PX}} = 2 \times 2\sqrt 6 = 4\sqrt 6 \cr} $$