In a triangle ABC, AD is the median .F is the point on AC such that line BF bisect AD at E .If AD is equal to 11 cm and AF is equal to 4cm ,find the measures of AC

Dear Student,

Please find below the solution to the asked query:

We form our diagram from given information , As :

Here , AD  =  11 cm , AF  =  4 cm and DG | | BF ,

In $∆$ ADG , EF | | DG (  As EF is part of BF and we construct DG  | | BF )

E is mid point of AD ,

From , Converse of mid point theorem we get " F "  is mid point of AG , So

AF =  FG                                                        ---- ( 1 )

And

In $∆$ CBF , BF | | DG (  As we construct DG  | | BF )

D is mid point of BC ,

From , Converse of mid point theorem we get " G "  is mid point of FC , So

FG =  GC                                                        ---- ( 2 )

From equation 1 and 2 we get

AF  =  FG  =  GC 

And

AC =  AF +  FG  +  GC , So

AC  = AF  +  AF  +  AF

AC  = 3 AF

AC  =  3 (  4 )

AC  =  12 cm                                                                      ( Ans )


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