खालील वर्तुळात, जीवा  ही अशाप्रकारे वाढवली जाते की ती वर स्पर्शिका  ला मिळेल. जर  आणि  , तर  ची लांबी शोधा.

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

Answer (Detailed Solution Below)

Option 3 : 4 सेमी
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Detailed Solution

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वापरलेली संकल्पना:

स्पर्शिका छेदक प्रमेयानुसार

DE2 = DB × DA

गणना:

DB × DA = DE2

⇒ DB × (5 + DB) = 62

⇒ DB × (5 + DB) = 36

⇒ 5DB + DB2 = 36

⇒ DB2 + 5DB - 36 = 0

वरील द्विघात समीकरण सोडवणे,

DB = (-9) किंवा DB = 4

लांबी ऋणात्मक असू शकत नाही, DB = 4 सेमी

∴ DB ची लांबी 4 सेमी आहे.

Shortcut Trick 

DB × (5 + DB) = 36

पर्याय तपासून आपण हे समीकरण कमी वेळेत सोडवू शकतो

अशा प्रकारे, पर्याय 03 समीकरणाचे समाधान करतो

∴ DB ची लांबी 4 सेमी आहे.

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