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PR is tangent to a circle, with centre O and radius 4 cm, at point Q. If ∠POR = 90°,OR = 5 cm and OP = 20/3 cm, then (in cm) the length of PR is :
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- 3
- 16 ÷ 3
- 23 ÷ 3
- 25 ÷ 3
- 3
Correct Option: D
According to question , we draw a figure of a circle with centre O ,
| Given that , ∠POR = 90°,OR = 5 cm and OP = | cm. | |
| 3 |
OQ ⊥ PR
∴ From ∆ OPQ,
PQ = √OP² - OQ²
| = √ |  |  | ² | - 4² | |
| 3 |
| PQ = √ | - 16 | |
| 9 |
| PQ = √ | |
| 9 |
| PQ = √ | |
| 9 |
| PQ = | cm. | |
| 3 |
From ∆ OQR,
QR = √OR² - OQ²
QR = √5² - 4² = √25 - 16 = √9 = 3 cm
| ∴ PR = PQ + QR = | + 3 = | cm | ||
| 3 | 3 |
