Question

In the adjoining figure,AD and BE are the median of triangle ABC and DF||BE Show that CF=1/2 AC​

Answer 1

Consider ΔABC

Since AD is Median ⟹BD=BC⋯(1)

Since BE is Median ⟹AE=EC⋯(2)

Consider ΔBEC

Since BE∣∣DF

By Basic Proportionality theorm,

⟹

DC

BD

=

FC

EF

From (1)

⟹CF=EF

⟹CF=

2

1

AE

From (2)

⟹CF=

4

1

AC