దిగువ వృత్తంలో, తీగ D వద్ద స్పర్శరేఖ  కలిసేలా పోడిగించబడుతుంది. ఒకవేళ మరియు పొడవును కనుగొనండి?

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RRB ALP Previous Paper 5 (Held On: 10 Aug 2018 Shift 3)
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  1. 6 సెం.మీ
  2. √30 సెం.మీ
  3. 4 సెం.మీ
  4. 5 సెం.మీ

Answer (Detailed Solution Below)

Option 3 : 4 సెం.మీ
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Detailed Solution

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ఉపయోగించిన భావన:

టాంజెంట్ సెకెంట్ సిద్ధాంతం ప్రకారం

DE 2 = DB × DA

గణన:

DB × DA = DE2

⇒ DB × (5 + DB) = 62

⇒ DB × (5 + DB) = 36

⇒ 5DB + DB2 = 36

⇒ DB2 + 5DB - 36 = 0

పై వర్గ సమీకరణాన్ని పరిష్కరించడం,

DB = (-9) లేదా DB = 4

పొడవు ప్రతికూలంగా ఉండకూడదు కాబట్టి, DB = 4 సెం.మీ

∴ DB పొడవు 4 సెం.మీ.

 Shortcut Trick

DB × (5 + DB) = 36

ఎంపికలను తనిఖీ చేయడం ద్వారా, మేము ఈ సమీకరణాన్ని తక్కువ సమయంలో పరిష్కరించగలము

అందువలన, ఎంపిక 03 సమీకరణాన్ని సంతృప్తిపరుస్తుంది

∴ DB పొడవు 4 సెం.మీ.

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