In Δ ABC, D and E are points on sides AB and BC, respectively, such that BD : DA = 1 : 2 and CE :EB = 1 : 4. If DC and AE intersect at F, then FD : FC is equal to:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 8 : 3.
G is the cevian of the triangle
DA/DB × BE/CE × CG/AG = 1
2/1 × 4/1= AG/CG
AG/CG = 8/1
So,
CF/FD = GC/AG + CE/BE
CF/FD = 1/8 + 1/4
= 3/8
FD : FC = 8 : 3