ΔDEF में, DE = 9 सेमी, EF = 12 सेमी तथा DF = 7 सेमी हैI यदि DO, ∠EDF का कोण समद्विभाजक है और EF से O पर मिलता है, तो OF की लंबाई ज्ञात कीजियेI

  1. 5.25 सेमी
  2. 4.35 सेमी
  3. 4.00 सेमी
  4. 4.25 सेमी

Answer (Detailed Solution Below)

Option 1 : 5.25 सेमी
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दिया गया है:

DE = 9, EF = 12 सेमी, तथा DF = 7 सेमी

DO, ∠EDF का कोण समद्विभाजक है

प्रयुक्त अवधारणा:

एक त्रिभुज में, यदि AD, ∠BAC का कोण समद्विभाजक है जो विपरीत भुजा BC को D पर काटता है तो

कोण समद्विभाजक प्रमेय के द्वारा

AB/AC = BD/CD

गणना:

DE = 9, EF = 12 सेमी, तथा DF = 7 सेमी

DO, ∠EDF का कोण समद्विभाजक है

कोण समद्विभाजक प्रमेय के द्वारा,

DE/DF = EO/OF

⇒ 9/7 = (EF - OF)/OF

⇒ 9/7 = (12 - OF)/OF

⇒ 9 × OF = 84 - 7 × OF

⇒ 16 × OF = 84

⇒ OF = 84/16

⇒ OF = 5.25 सेमी

OF का मान 5.25 सेमी हैI

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