In triangle \( \triangle ABC \), AD is a median. Point E divides AD in the ratio 1:2. The extended line BE intersects AC at point F. If \( AC = 10 \) cm, find the length of \( AF \).

Q.In triangle \( \triangle ABC \), AD is a median. Point E divides AD in the ratio 1:2. The extended line BE intersects AC at point F. If \( AC = 10 \) cm, find the length of \( AF \). (a) 5 cm (b) 4 cm (c) 2 cm (d) None of the above

Answer: C

If a line is drawn through point D parallel to BF, it intersects AC at point G. In triangle \( \triangle ADG \), EF is parallel to DG. ∴ \( AF : FG = AE : ED = 1 : 2 \) Again, in triangle \( \triangle FBC \), BF is parallel to DG. ∴ \( FG : GC = BD : DC = 1 : 1 \) (because AD is a median) ∴ \( AF : FG : GC = 1 : 2 : 2 \) ∴ \( AF = \frac{1}{5} \times AC = 2 \) cm