निम्नलिखित आकृति में, O वृत्त का केंद्र है। इसकी दो जीवाएँ AB और CD वृत्त के अंदर बिंदु P पर एक दूसरे को प्रतिच्छेद करती हैं। यदि AB = 18 सेमी, PB = 6 सेमी और CP = 4 सेमी है, तो PD का माप ज्ञात कीजिए।

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SSC CGL 2023 Tier-I Official Paper (Held On: 27 Jul 2023 Shift 1)
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  1. 14 सेमी 
  2. 18 सेमी 
  3. 16 सेमी 
  4. 20 सेमी 

Answer (Detailed Solution Below)

Option 2 : 18 सेमी 
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दिया गया है:-

दो जीवाएँ AB और CD एक दूसरे को बिंदु P पर प्रतिच्छेद करती हैं।

AB = 18 सेमी, PB = 6 सेमी, और CP = 4 सेमी

प्रयुक्त सूत्र:-
 

यदि दो जीवाएँ AB और CD वृत्त के अंदर बिंदु P पर एक दूसरे को प्रतिच्छेद करती हैं,
तब, AP × PB = CP × PD

गणना:-

AP = AB - PB

⇒ AP = 18 - 6 = 12 सेमी

सूत्र के अनुसार

AP × PB = CP × PD

⇒ 12 × 6 = 4 × PD

⇒ PD = 72/4

∴ अभीष्ट उत्तर 18 है।

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