solution-of-triangles-8

Hard

Q-1: The internal bisectors of the angles of the DABC meet the sides BC, CA and AB at P, Q, and R respectively. Show that the area of the DPQR is equal to

Solution:

Let the bisector of the angles meet at I. then I is the incenter. Let ID^BC, then ID = inradius = r.

Q=ÐBIP-ÐBID =

Fig (24)

Now from DDIP,

 

 

 

Q-2: Show that the DABC is equilateral if its circumradius is double of the inradius.

Solution:

Here R=2r (given) .We know that,

So, triangle is equilateral.