त्रिभुज ABC में, कोण BAC का समद्विभाजक, भुजा BC को D पर काटता है। यदि AB = 10 सेमी, और AC = 14 सेमी है, तो BD : BC का मान क्या है?

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SSC CGL 2022 Tier-I Official Paper (Held On : 05 Dec 2022 Shift 1)
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  1. 5 : 3
  2. 7 : 5
  3. 5 : 2
  4. 5 : 12

Answer (Detailed Solution Below)

Option 4 : 5 : 12
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दिया गया है:

AB = 10 सेमी, और AC = 14 सेमी

प्रयुक्त अवधारणा:

त्रिभुज का कोण समद्विभाजक सम्मुख भुजा को त्रिभुज की अन्य दो भुजाओं के समानुपाती दो भागों में विभाजित करता है।

गणना:

F1 SSC Amit A 24-02-2023 D9

अवधारणा के अनुसार,

AB/AC = BD/DC

⇒ 10/14 = BD/DC

⇒ 5/7 = BD/DC

इसलिए, BD : DC = 5 : 7

अब, BC = 5 + 7

⇒ 12

इसलिए, BD : BC = 5 : 12

∴ अभीष्ट उत्तर 5 : 12 है।

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