O is any point in the interior of `DeltaABC`. Bisectors of `/_AOB, BOC` and AOC intersect sideAB, side BC, side AC in F,D and E respectively.
Prove that `BFxxAExxCD=AFxxCExxBD`.

O is any point inside a triangle ABC. The bisector of /_AOB,/_BOC and /_COA meet the sides AB,BC and CA in point D, and F respectively.Show that ADxBExCF =DBxECFA

O is any point inside a triangle ABC. The bisector of angle AOB, angle BOC and angle COA meet the sides AB, BC and CA in point D, E and F respectively. Show that AD xx BE xx CF= DB xx EC xx FA

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 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 .

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

DeltaABC and DeltaDBC are situated on the same base BC and on the same side of BC . E is any point on the side BC . Two line through the point E and parallel to AB and BD intersects the sides AC and DC at the points F and G respectively. Prove that AD||FG .

The incircle of an isosceles triangle ABC , with AB=AC , touches the sides AB , BC , CA at D,E and F respectively. Prove that E bisects BC .

D is any point on the side BC of DeltaABC . P and Q are centroids of DeltaABD and DeltaADC respectively. Prove that PQ||BC .