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PT అనేది O మరియు OP = 17 సెం.మీ మరియు OT = 8 సెం.మీ ఉన్న వృత్తం యొక్క Tకి టాంజెంట్ అయితే, టాంజెంట్ లైన్ సెగ్మెంట్ PT పొడవును కనుగొనండి.

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

Answer (Detailed Solution Below)

Option 4 : 15 సెం.మీ
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Detailed Solution

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ఇచ్చినవి:

PT అనేది వృత్తానికి టాంజెంట్, దీని కేంద్రం O

OP = 17 సెం.మీ

OT = 8 సెం.మీ

ఉపయోగించిన సూత్రము:

పైథాగరస్ సిద్ధాంతం: లంబకోణ త్రిభుజంలో, కర్ణం సమానం - 

OP2 = OT2 + TP2

గణన​:

ఇది, టాంజెంట్ TP యొక్క పొడవు సమానంగా ఉంటుంది:

TP2 = OP2 - OT2  

TP2 = (17)2 - (8)2  

TP2 = 289 - 64

TP2 = 225 

TP = √225 = 15

∴ టాంజెంట్ సెగ్మెంట్ PT పొడవు 15 సెం.మీ.కి సమానం.

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