Question

6. In the below figure the circle touches all the sides of a quadrilateral ABCD whose three sides are AB = 6 cm BC = 7 cm , CD = 4 cm Find AD​

Answer 1

Answer: Given : A circle inscribed in a quadrilateral ABCD,AB=6cm,BC=7cm,CD=4cm.

To find : AD

Proof : Let the circle touch the sides AB,BC,CD,DA, at P,Q,R and S, respectively.

AP=AS          

BP=BQ                      

DR=DS                    

CR=CQ  

Adding all these, we get

(AP+BP)+(CR+RD)=(BQ+QC)+(DS+SA)

AB+CD=BC+DA

⇒6+4=7+AD

⇒AD=10−7=3cm.

Answer 2

1. only we have to + seee 6+7+4-17