Question
Download Solution PDFIn ΔDEF, DE = 9 cm, EF = 12 cm and DF = 7 cm. If DO is the angle bisector of ∠EDF meets EF at O, then find the length of OF.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
DE = 9, EF = 12 cm, and DF = 7 cm
DO is the angle bisector of ∠EDF
Concept used:
In a triangle, If AD is the angle bisector of ∠BAC intersect the opposite side BC at D then
By angle bisector theorem
AB/AC = BD/CD
Calculation:
DE = 9, EF = 12 cm, and DF = 7 cm
DO is the angle bisector of ∠EDF
By angle bisector theorem,
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 cm
∴ The value of OF is 5.25 cm.
Last updated on Jul 8, 2025
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