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Two circles whose radii are 10 cm and 8 cm, intersect each other and their common chord is 12 cm long. What is the distance between their centres ?
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- 11.27 cm
- 12.29 cm
- 12.27 cm
- 13.29 cm
- 11.27 cm
Correct Option: D
According to question , we draw a figure of two circles whose radii are 10 cm and 8 cm, intersect each other and their common chord is 12 cm long
OP = 10 cm, O’P = 8 cm and PQ = 12 cm ;
| PL = | PQ = 6 cm | 2 |
In right angled ∆ OLP,
OL = √OP² - LP²
OL = √10² - 6² = √64 = 8 cm
In ∆ O'LP,
O'P² = O'L² + LP²
⇒ O'L = √O'P² - LP²
O'L = √8² - 6² = √28 = 5.29 cm
∴ OO' = OL + LO' = 8 + 5.29 = 13.29 cm
