यदि एक वृत्त का क्षेत्रफल 616 सेमी2 है और जीवा XY = 10 सेमी है, तो वृत्त के केंद्र से जीवा XY की लंबवत दूरी ज्ञात कीजिए।

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SSC CGL 2023 Tier-I Official Paper (Held On: 17 Jul 2023 Shift 1)
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  1. \(\sqrt{171}\) सेमी
  2. \(\sqrt{161}\) सेमी
  3. \(\sqrt{117}\) सेमी
  4. \(\sqrt{181}\) सेमी

Answer (Detailed Solution Below)

Option 1 : \(\sqrt{171}\) सेमी
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दिया गया है:

वृत्त का क्षेत्रफल = 616 सेमी2

जीवा = XY = 10 सेमी

प्रयुक्त अवधारणा:

केंद्र से लंबवत रेखा जीवा को दो बराबर भागों में विभाजित करती है।

प्रयुक्त सूत्र:

पाइथागोरस प्रमेय:

H2 = P2 + B2

जहाँ, H = कर्ण; P = लंब; B = आधार 

वृत्त का क्षेत्रफल = π × R2

गणना:

F1 SSC Arbaz 6-10-23 D18

वृत्त का क्षेत्रफल = 616 सेमी2

⇒ π × R2 = 616

⇒ R2 = (616 × 7)/22

⇒ R = √(28 × 7) = 14 सेमी 

OX = 14 सेमी

XY = 10 सेमी

OC ⊥ XY

XC = 10/2 = 5 सेमी

पाइथागोरस प्रमेय द्वारा

⇒ H2 = P2 + B2 

⇒ (OX)2 = (OC)2 + (XC)2

⇒ (14)2 = (OC)2 + (5)2

⇒ (OC)2 = 196 - 25 = 171

⇒ OC = √171

∴ सही उत्तर √171 है।

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