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వ్యాసార్థం 16 సెం.మీ మరియు 8 సెం.మీ ఉన్న రెండు వృత్తాల కేంద్రాల మధ్య దూరం 26 సెం.మీ. రెండు వృత్తాల యొక్క ప్రత్యక్ష సాధారణ స్పర్శరేఖ యొక్క పొడవు (సెం.మీ.లో):

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SSC CGL 2023 Tier-I Official Paper (Held On: 17 Jul 2023 Shift 3)
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  1. \(2\sqrt{132}\)
  2. \(\sqrt{153}\)
  3. \(2\sqrt{153}\)
  4. \(\sqrt{132}\)

Answer (Detailed Solution Below)

Option 3 : \(2\sqrt{153}\)
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Detailed Solution

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ఇచ్చిన సమస్య:-
 
పెద్ద వృత్తం యొక్క వ్యాసార్థం (R) = 16 సెం.మీ
 
చిన్న వృత్తం యొక్క వ్యాసార్థం (r) = 8 సెం.మీ
 
మధ్య దూరం (D) = 26 సెం.మీ
 
ఉపయోగించిన సూత్రం:
 
ప్రత్యక్ష సాధారణ స్పర్శరేఖ = √{D2 - (R - r)2}
 
సాధన:
 
ప్రత్యక్ష సాధారణ స్పర్శరేఖ = √{D2 - (R - r)2}
 
⇒ √{262 - (16 - 8)2}
 
⇒ √{676 - 64} = √612 = 2 × √153
 
∴ సరైన సమాధానం 2√153.
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