`A B C` is a triangle. The bisector of the exterior angle at `B` and the bisector of `/_C` intersect each other at `D`. Prove that `/_D=1/2/_A`.

In triangle LMN, bisector of interior angles at L and N intersect each other at point A. Prove that : AM bisects angle LMN.

Bisectors of interior /_ B and exterior /_ ACD of a Delta ABC intersect at the point T . prove that /_BTC = 1/2 /_ BAC .

In A B C ,/_B=2/_C and the bisector of /_B intersects A C at Ddot Prove that (B D)/(D A)=(B C)/(B A)

DeltaABC is a right triangle right angled at A such that AB = AC and bisector of /_C intersects the side AB at D . Prove that AC + AD = BC .

In parallelogram ABCD, the bisectors of adjacent angles A and D intersect each other at point P. prove that angleAPD=90^(@) .

In a parallelogram A B C D , the bisector of /_A also bisects B C at X . Prove that A D=2A B .

Construct a triangle ABC which angle ABC=75^(@), AB=5" cm"and BC =6.4" cm" . Draw perpendicular bisector of side BC and also the bisector of angle ACB. If these bisector intersect each other at point P, prove that P is equidistant from B and C, and also from AC and BC.

The sides A B and A C of A B C are product to P and Q\ respectively. the bisectors of exterior angles at B and C of A B C meet at O\ (fig.19) prove that /_B O C=90^0-1/2/_A

In a quadrilateral ABCD , CO and DO are the bisectors of /_C and /_D respectively. Prove that /_C O D=1/2(/_A+/_B)

In a triangle A B C , the internal bisectors of /_B\ a n d\ /_C meet at P and the external bisectors of /_B\ a n d\ /_C meet at Q . Prove that /_B P C+\ /_B Q C=180^0