Prove that bd/cd = bf/ce, Mathematics

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In the given figure, ∠AEF=∠AFE and E is the mid-point of CA. Prove that BD/CD = BF/CE

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Ans:    Draw CG ¦DF In ΔBDF

CG ¦ DF

BD/CD = BF/GF     .............(1)               BPT

In ΔAFE

∠AEF=∠AFE

⇒AF=AE

⇒AF=AE=CE..............(2)

In ΔACG

E is the mid point of AC

⇒ FG = AF

∴ From (1) & (2)

BD/CD     =     BF/CE

Hence proved


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