Question
Download Solution PDFयदि 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।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया 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:
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।
Last updated on Jul 10, 2025
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