ABCD is parallelogram A circle passing through the points A and B intersect the sides AD and BC at the points E and F repectively . Prove that the four points E, F , C ,D are concyclic.

ABCD is a parallelogram. A circle passing through C and D intersects AD and BC at the points E and F. Prove that the four points E, A, B, F are concyclic.

In Figure,ABCD is a cyclic quadrilateral.A circle passing through A and B meets AD and BC in the points E and F respectively.Prove that EFDC

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.

ABCD is a cyclic quadrilateral. A circle passing through A and B meets AD and BC in E and F respectively. Prove that EF||DC

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 .

ABCD is a parallelogram . The circle passing through the vertices. A, B and C intersects CD (or CD produced) at E. Prove that AE=AD .

ABCD is a parallelogram . The circle passing through the vertices. A, B and C intersects CD (or CD produced) at E. Prove that AE=AD .

ABCD is a parallelogram.The circle through A,B and C intersects CD produced at E, prove that AE=AD

In DeltaABC , AB =AC , BE and CF are the bisectors of the angles angleABCandangleACB and they intersect AC and AB at the points E and F respectively. Then four points B ,C ,E , F are not concyclic.