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Question
In the following figure, DE || AC and DF || AE. Prove that `("BF")/("FE") = ("BE")/("EC")`
Solution
In ΔABC, DE || AC
∴ `("BD")/("DA") = ("BE")/("EC")` ...(Basic Proportionality Theorem) ...(i)
In ΔBAE, DF || AE
∴ `("BD")/("DA") = ("BF")/("FE")` ...(Basic Proportionality Theorem) ....(ii)
∴ From (i) and (ii) we obtain
`("BE")/("EC") = ("BF")/("FE")`
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