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Triangle PQR circumscribes a circle with centre O and radius r cm such that ∠PQR = 90°. If PQ = 3 cm, QR = 4 cm, then the value of r is :
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- 2
- 1.5
- 2.5
- 1
- 2
Correct Option: D
According to question , we draw a figure of triangle PQR circumscribes a circle with centre O
Given that , ∠PQR = 90° , PQ = 3 cm, QR = 4 cm
PR² = PQ² + PR²
PR² = 3² + 4² = 2²
∴ PR = √25 = 5 cm
| We know that , r = | |
| Semi perimeter of triangle |
| r = | × 3 × 4 | |
| 2 | ||
| 2 | ||
| r = | = 1 cm | |
| 6 |
Second method :
In the above figure, QR = r + 2 + r = 4
⇒ 2r = 4 - 2 = 2
⇒ r = 1
