[ABCD" is a square.The bisector of "/_DBC" cuts "AC],[" and "CD" at "E" and "F" respectively.Prove that "],[BF times CE=BE times DF]

AD is a median of Delta ABC. The bisector of /_ADB and /_ADC meet AB and AC in E and F respectively.Prove that EF |BC

In triangle ABC, angleABC=angleACB . The bisectors of angleABCandangleACB intersect AC and AB at E and F respectively. Prove that FE||BC.

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 angleB and angleC meet AC and AB at point D and E respectively. Prove that BD = CE .

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.

AD is a median of triangleABC . The bisectors of angleADB and angleADC meets AB and AC in E and F respectively prove that EF||BC.

ABCD is a cyclic quarilateral. The bisectors of angleaandangleC in tersect the circle at the points E and F respectively . Prove that EF is a diameter of the circle.

In the fig ABCD is a parallelogram in which E and F are mid points of AB and CD respectively. Prove that the line segments CE and AF intersect diagonal BD

In squareABCD , side AB~= side AD. Bisector of /_BAC cuts side BC at E and bisector of /_DAC cuts side CD at F. Prove that set EF|| seg BD.

ABCD is a quadrilateral in which AD = BC. E, F, G and H are the mid-points of AB, BD, CD and AC respectively. Prove that EFGH is a rhombus.