In triangle ABC, side AC is greater than side AB. If the internal bisector of angle A meets the opposite side at point D, prove that : `angleADC` is greater than `angleADB`.

If the bisector of an angle of a triangle bisects the opposite side, prove that the triangle is isosceles.

In DeltaABC , angle ABC is equal to twice the angle ACB, and bisector of angle ABC meets the opposite side at point P. Show that : CB : BA = CP : PA

In DeltaABC , angle ABC is equal to twice the angle ACB, and bisector of angle ABC meets the opposite side at point P. Show that : AB xx BC = BP xx CA

In a triangle ABC , AB = AC and angle A = 36^(@) If the internal bisector of angle C meets AB at D . Prove that AD = BC.

In a triangle ABC the sides BC=5, CA=4 and AB=3 . If A(0,0) and the internal bisector of angle A meets BC in D (12/7,12/7) then incenter of triangle ABC is

In a triangle ABC, side AC is greater than side AB and point D lies on side BC such that AD bisects angle BAC. Show that: angle ADB is acute.

Let triangle ABC be an isosceles with AB=AC. Suppose that the angle bisector of its angle B meets the side AC at a point D and that BC=BD+AD . Measure of the angle A in degrees, is :

In the given figure, AB = AC. Prove that AF is greater than AE.

ABC is a right triangle with AB = AC .If bisector of angle A meet BC at D then prove that BC = 2 AD .

The given figure shows a triangle ABC in which AD bisects angle BAC. EG is perpendicular bisector of side AB which intersects AD at point F. Prove that : F is equidistant from AB and AC.