ΔABC में D, BC पर एक बिंदु है। AB को E तक बढ़ाया जाता है और AC को F तक बढ़ाया जाता है। एक वृत्त DEF से होकर गुजरता है जहाँ AB = 10 सेमी, AC = 8.6 सेमी और BC = 6.4, तो BE = ?

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SSC CGL Tier 2 Quant Previous Paper 6 (Held On: 13 September 2019)
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  1. 3.5 सेमी
  2. 3.2 सेमी
  3. 2.5 सेमी
  4. 2.2 सेमी

Answer (Detailed Solution Below)

Option 3 : 2.5 सेमी
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संकल्पना:

समान बाह्य बिंदु से एक वृत्त के लिए स्पर्शरेखा खंड बराबर होते हैं।

गणना:

दिया है, AB = 10 सेमी, AC = 8.6 सेमी और BC = 6.4 सेमी

माना BE = x सेमी और CF = y सेमी 

जैसा कि हम जानते हैं,

BE = BD [स्पर्शरेखाएँ]

DC = CF [स्पर्शरेखाएँ]

AE = AF [स्पर्शरेखाएँ]

AB + BE = AC + CF

⇒ 10 + x = 8.6 + y

⇒ x – y = 8.6 – 10

⇒ x – y = - 1.4         ----(1)

BD + DC = 6.4

⇒ x + y = 6.4         ----(2)

समीकरण (1) और समीकरण (2) से

⇒ x = 2.5

∴  BE = 2.5 cm

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