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AC is transverse common tangent to two circles with centres P and Q and radii 6 cm and 3 cm at the point A and C respectively. If AC cuts PQ at the point B and AB = 8cm then the length of PQ is :
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- 13 cm
- 12 cm
- 10 cm
- 15 cm
- 13 cm
Correct Option: D
On the basis of question we draw a figure of two circles with centres P and Q and radii 6 cm and 3 cm at the point A and C respectively ,
In ∆ APB and ∆ BCQ,
∠ PAB = ∠ BCQ = 90°
∠ PBA = ∠ QBC
By AA – similarity,
∆ APB ~ ∆ BQC
| ∴ | = | ||
| BC | QC |
| ⇒ | = | ||
| BC | 3 |
| ⇒ BC = | = 4 cm. | |
| 6 |
∴ PQ = √AC² + (r1 + r2)²
PQ = √(8 + 4)² + (6 + 3)²
PQ = √12² + 9² = √144 + 81
PQ = √225 = 15 cm.
