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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
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- 2 √13 cm.
- 5√3 cm.
- 4√6 cm.
- 6√5 cm
- 2 √13 cm.
Correct Option: C
According to question , we draw a figure of a circle with centre O , 
Here , AX : BX = 3 : 2
| = | ||
| BX | 2 |
| ∴ AX = | × 10 = 6 cm. | |
| 5 |
| ∴ BX = | × 10 = 4 cm. | |
| 5 |
∴ AX × XB = PX²
⇒ PX² = 6 × 4
⇒ PX = √6 × 4 = 2 √6
∴ PQ = 2PX = 4√6 cm.
