Question

In the given figure d,e,f are the mid points of BC,CA and AB respectively if the angle between tangent A,B is 60° find angle CDF

Answer 1

Answer:

Since D and E are the mid-points of the sides BC and AB respectively of △ABC.  

Therefore,

           DE∣∣BA

⇒ DE∣∣FA........(i)

Since D and F are mid-points of the sides BC and AB respectively of △ABC.

    ∴  DF∣∣CA⇒DF∣∣AE.......(ii)

From (i), and (ii), we conclude that AFDE is a parallelogram.

Similarly, BDEF is a parallelogram.

Now, in △DEF and △ABC, we have

          ∠FDE=∠A            [Opposite angles of parallelogram AFDE)

and,  ∠DEF=∠B             [Opposite angles of parallelogram BDEF]

So, by AA-similarity criterion, we have

     △DEf∼△ABC

⇒  

ARE(△ABC)

Area(△DEF)

​  

=  

AB  

2

 

DE  

2

 

​  

=  

AB  

2

 

(1/2AB)  

2

 

​  

=  

4

1

​  

           [∵DE=  

2

1

​  

AB]

Hence, Area(△DEF):Area(△ABC)=1:4

Step-by-step explanation: