18 सेमी त्रिज्या वाले दो समान वृत्त एक दूसरे को इस प्रकार प्रतिच्छेद करते हैं कि प्रत्येक दूसरे के केंद्र से होकर गुजरते हैं। उभयनिष्ठ जीवा की लंबाई _________ है।

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SSC CGL 2023 Tier-I Official Paper (Held On: 24 Jul 2023 Shift 4)
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  1. \(6\sqrt{27}\) सेमी 
  2. \(9\sqrt{27}\) सेमी 
  3. \(\sqrt{3}\)
  4. \(3\sqrt{3}\) सेमी 

Answer (Detailed Solution Below)

Option 1 : \(6\sqrt{27}\) सेमी 
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दिया गया है:

वृत्तों की त्रिज्याएँ 18 सेमी है।

गणना:

F1 ArunK Madhuri 11.03.2022 D6

आरेख के अनुसार,

AD = DB

O1O2 = 18

पुन: O1A = O2A = 18 [वृत्त की त्रिज्या]

∠ADO1 = 90°

O1D = O2D = 9

AD = √(324 - 81)

⇒ (9√3)

AB = 2 × (9√3) = 18√3 = 6√27

∴ उभयनिष्ठ जीवा की लंबाई 6√27 सेमी है।

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