यदि PT उस वृत्त के बिंदु T पर स्पर्श रेखा है जिसका केंद्र O है और OP = 17 सेमी तथा OT = 8 सेमी है, तो स्पर्श रेखा खंड PT की लंबाई ज्ञात कीजिए।

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SSC CGL 2022 Tier-I Official Paper (Held On : 09 Dec 2022 Shift 1)
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  1. 13 सेमी 
  2. 14 सेमी 
  3. 16 सेमी
  4. 15 सेमी 

Answer (Detailed Solution Below)

Option 4 : 15 सेमी 
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दिया गया है:

PT एक वृत्त की स्पर्श रेखा है, जिसका केंद्र O है।

OP  = 17 सेमी

OT = 8 सेमी

प्रयुक्त सूत्र:

Screenshot 2023-02-27 184313

पाइथागोरस प्रमेय: एक समकोण त्रिभुज में, कर्ण बराबर होता है -

 OP2 = OT2 + TP2

गणना:

यह, स्पर्शरेखा TP की लंबाई बराबर है:

TPOP2 - OT2  

TP(17)2 - (8)2  

TP= 289 - 64

TP= 225 

TP = 225 = 15

स्पर्श रेखाखंड PT की लंबाई 15 सेमी के बराबर है।

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