एक वृत्त के केंद्र के एक ही तरफ दो समानांतर जीवाएँ AB = 28 सेमी और CD = 22 सेमी हैं। उनके बीच की दूरी 4 सेमी है। वृत्त की त्रिज्या कितनी है? (दो दशमलव तक पूर्णांकित कीजिए)

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SSC CGL 2023 Tier-I Official Paper (Held On: 21 Jul 2023 Shift 2)
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  1. 15.20 सेमी
  2. 14.82 सेमी
  3. 15.82 सेमी
  4. 13.20 सेमी

Answer (Detailed Solution Below)

Option 3 : 15.82 सेमी
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PYST 1: SSC CGL - English (Held On : 11 April 2022 Shift 1)
25 Qs. 50 Marks 12 Mins

Detailed Solution

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दिया गया है:

एक वृत्त के केंद्र के एक ही तरफ दो समानांतर जीवाएँ AB = 28 सेमी और CD = 22 सेमी हैं।

उनके बीच की दूरी 4 सेमी है।

गणना:

माना, OE की लंबाई x है, EF = 4 सेमी 

प्रश्न के अनुसार,

OA = OC

⇒ 142 + x2 = (x+4)2 + 112

⇒ 196 + x2 = x2 + 16 + 8x + 121

⇒ 8x = 59

x = 59 / 8 

त्रिज्या का मान होगा:

√(142 + () 2 = 15.82 सेमी

∴ सही उत्तर विकल्प 3 है। 

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