From the given figure prove that: AP + BQ + CR = BP + CQ + AR. Also, show that AP + BQ + CR = ½ x perimeter of triangle ABC.

Solution:

From point

   

are the tangents to the circle

We have,

   

Similarly, we also get

   

And,

   

Adding

   

we get,

   

Now, adding

   

to both sides in

   

we get

   

   

   

   

Therefore, we get

   

   

That is,