If a quadrilateral ABCD, the bisector of `angleC angleD` intersect at O.
Prove that `angleCOD=(1)/(2)(angleA+angleB)`

ABCD is a quadrilateral in which AB= AD, the bisector of angle BAC and angle CAD intersect the sides BC and CD at the points E and F respectively. Prove that EF || BD.

In a parallelogram ABCD, the bisectors of the consecutive angles angleA and angleB intersect at P. Show that angleAPB=90^(@) .

In quadrilateral ABCD, AB=AD, AC bisects angleA . Prove DeltaABC~ADC .

In a cyclic quadrilateral ABCD, the bisectors of opposite angles A and C meet the circle at Pand Q respectively. Prove that PQ is a diameter of the circle.

In the given figure, ABCD is a cyclic quadrilateral where diagonals intersect at P such that angleDBC=40^(@) and angleBAC=60^(@) find (i) angleCAD (ii) angleBCD