8 सेमी त्रिज्या वाले दो समान वृत्त एक दूसरे को इस प्रकार प्रतिच्छेद करते हैं कि दोनों एक-दूसरे के केंद्र से होकर गुजरते हैं। उभयनिष्ठ जीवा की लंबाई कितनी है?

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SSC CGL 2022 Tier-I Official Paper (Held On : 01 Dec 2022 Shift 4)
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  1. \(8\sqrt3\) सेमी
  2. \(\sqrt 3\) सेमी
  3. \(2\sqrt3\) सेमी
  4. \(4\sqrt3\) सेमी

Answer (Detailed Solution Below)

Option 1 : \(8\sqrt3\) सेमी
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दिया गया है:

वृत्तों की त्रिज्या 8 सेमी है।

गणना:

F1 ArunK Madhuri 11.03.2022 D6

आरेख के अनुसार,

AD = DB

O1O2 = 8

पुनः O1A = O2A = 8 [वृत्त की त्रिज्या]

∠ADO1 = 90°

O1D = O2D = 4

AD = √(64 - 16)

⇒ √48 = 4√3

AB = 2 × 4√3 = 8√3

∴ उभयनिष्ठ जीवा की लंबाई 8√3 सेमी है।

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