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

In the adjoining figure, BM and DN are the perpendiculars from B and D respectively to AC such that BM = DN. Prove that BO = OD.

In the adjoining figure, BM and CN are the altitudes drawn to the sides AC and AB respectively of DeltaABC . If BM=CN, prove that DeltaABC is isosceles.

In the adjoining figure, OX and RX are the bisectors of the angle Q and R respectively of the triangle PQR. If XS bot QR and XTbotPQ . Prove that : DeltaXTQ~=DeltaXSQ

In the adjoining figure, OX and RX are the bisectors of the angle Q and R respectively of the triangle PQR. If XS bot QR and XTbotPQ . Prove that : PX bisects angle P.

In the adjoining figure, QX and RX are the bisectors of the angles Q and R respectively of the angles Q and R respectively of the triangle PQR. If XS bot PQ . Prove that : (i) DeltaXTQ cong DeltaXSQ (ii) PX bisects angle P.

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 the given figure AC = BD, prove that AB = CD.

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

In following figure if AD if the bisector of angleABC, then prove that AB gt BD