Question
Download Solution PDFΔDEF 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
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया 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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