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.

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.

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.

In Delta ABC,AB= AC, BE and CF are resepectively the bisectors of angle ABC and angle ACB and itersect the sides AC and AB at the points E and F resepectively. Then four points B,C,E,F are not concylic.

In trapezium ABCD , AB and DC are parallel. A straight line parallel to AB intersects AD and BC at the points E and F respectively. Prove that DE:EA=CF:FB .

The diagonals AC and BD of the parallelogram ABCD intersect each other at O . Any straight line passing through O intesects the sides AB and CD at the points P and Q respectively . Prove that OP = OQ.

In two circles , one circle passes through the centre O of the other circle and they intersect each other at the points A and B . A straight line passing through A intersect the circle passing through O at the point P and the circle with centre at O at the point R . BY joining P , B and R , B prove that PR= PB.

In the adjoining figure AD and BE are perpendicular ot BC and AC respectively of the Delta ABC . The four points A,B,D,E are concylic.

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.

DeltaABC is inscribed in a circle, AD is a diameter of the circle and AE is perpendicular on the side BC , which intersects the side BC at the point E . Prove that DeltaAEB and DeltaACD are similar. From this also prove that ABxxAC=AExxAD .