Question

In the given figure BD:CD=3:4 and AE=6BE, then CF:AF=?​

Answer 1

Answer:

option A  : 2/9

Step-by-step explanation:

In the given figure BD:CD=3:4 and AE=6BE, then CF:AF=?​

in Δ BDE

BD/ Sin ∠E  = BE /Sin∠D

=> Sin∠D / Sin ∠E  = BE /BD      ∠D = ∠BDE

in Δ AEF

AE/Sin∠F = AF/Sin∠E

=> AF  = AE Sin∠E / Sin∠F    ∠F = ∠AFD

in Δ CFD  

 ∠CFD  = 180 - ∠AFD    

∠CDF = ∠BDE = ∠D   (opposite angles)

CF/Sin∠D = CD/ Sin∠(180- F)        

=> CF = CD Sin∠D / Sin∠F     (Sinθ = Sin(180-θ) )

CF/ AF  = (CD Sin∠D) / (AE Sin∠E)

=> CF/ AF  = (CD/AE) * (Sin∠D / Sin∠E)

Using Sin∠D / Sin ∠E  = BE /BD

=> CF/ AF  = (CD/AE) * (BE / BD)

=> CF/ AF  = (CD/BD) * (BE / AE)

Using BD : CD = 3: 4 so CD/BD = 4/3

AE = 6BE

=> CF/AF = (4/3) * (BE/6BE)

=> CF/AF = (4/3) * (1/6)

=> CF/AF = 4/18

=> CF/AF = 2/9

option A is right answer (2/9)