In `DeltaABC, AB = AC` and the bisectors of `angleB` and `angleC` meet AC and AB at point D and E respectively. Prove that `BD = CE`.

In DeltaABC,AB=AC and the bisectors of angles B and C intersect at point O. Prove that BO=OC

A D is a median of Delta A B C . The bisector of /_A D B and /_A D C meet AB and AC in E and F respectively. Prove that EF||BC

In the adjoining figure, AB gt AC and the angle bisectors of angleB and angleC meet at point P. Prove that PB gt PC .

In triangleABC the bisector of angleB meets AC at D. A line PQ||AC meets AB,BC and BD at P, Q and R respectively. show that PRxxBQ = QRxxBP .

ABCD is a quadrilateral in which AB=AD . The bisector of BAC and CAD intersect the sides BC and CD at the points E and F respectively. Prove that EF||BD.

In the adjoining figure BO and CO are the bisectors of angleCBD and angleBCE respectively. If AC gt AB , prove that OB gt OC .

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 Delta ABC, if AB=AC and angleB=50^(@), " then " angleC is equal to

The bisector of interior angleA of triangleABC meets BC in D, and the bisector of exterior angle angleA meets BC produced in E. prove that (BD)/(BE)= (CD)/(CE)

The side AC of a triangle ABC is produced to point E so that CE=(1)/(2) AC. D is the mid-point of BC and ED produced meets AB at F. Lines through D and C are drawn parallel to AB which meet AC at point P and EF at point R respectively. Prove that: 3DF=EF