एक समद्विबाहु ΔMNP एक वृत्त में उत्कीर्ण है। यदि MN = MP = \(16\sqrt{5}\) सेमी, और NP = 32 सेमी, वृत्त की त्रिज्या (सेमी में) कितनी है?

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SSC CGL 2021 Tier-I (Held On : 13 April 2022 Shift 3)
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  1. 18
  2. \(20\sqrt{5}\)
  3. \(18\sqrt{5}\)
  4. 20

Answer (Detailed Solution Below)

Option 4 : 20
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दिया गया है:

MN = MP = 16√5 सेमी

NP = 32 सेमी

प्रयुक्त सूत्र:

त्रिभुज का क्षेत्रफल = (1/2) × आधार × ऊँचाई

परित्रिज्या = ABC/4Δ

जहाँ A, B और C त्रिभुज की तीन भुजाएँ हैं

Δ = त्रिभुज का क्षेत्रफल

गणना:

F1 Madhuri SSC 22.06.2022 D16

MD, NP पर लम्ब है

तो, ND = DP = 32/2 = 16 सेमी

MD = √[(16√5)2 - (16)2] = √(1280 - 256) = √1024 = 32 सेमी

ΔMNP का क्षेत्रफल = (1/2) × 32 × 32 = 512 वर्गसेमी

परित्रिज्या = (16√5 × 16√5 × 32)/(4 × 512) = 20 सेमी

∴ वृत्त की त्रिज्या (सेमी में) 20 सेमी है

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