UPSC 2017 CDS II Math Paper

In ΔABC, BE is the median.
Therefore, E is the mid-point of AC.
⇒AE=EC=

AC

2

...(1)
Also, AD is the median. So, D is the mid-point of BC.
In ΔBCE D is the mid-point of BC and DF||BE.
Therefore, F is the mid-point of EC. (Converse of mid-point theorem)
⇒CF=EF=

EC

2

...(2)
From (1) and (2), we have
CF=

EC

2

=

( AC 2 )

2

=

AC

4

∴CF=

9

4

=2.25cm