In cyclic quadrilateral ABCD, A^=80∘. Find the magnitude of C^.

In cyclic quadrilateral PQRS, the side PQ is produced to T. If TQ^​R=110∘, find the magnitude of PS^R.

In the given figure, O is the centre of the circle. If AO^C=130∘, find the value of AB^C.

Prove that a parallelogram inscribed in a circle is a rectangle.

In cyclic quadrilateral ABCD, if AB || DC, prove that AD = BC.

The side AD of a cyclic quadrilateral ABCD is produced to E. If CD^E=85∘ and DC^A=40∘, find CA^B.

ABCD is a cyclic quadrilateral. If A^=2x, B^=3y, C^=3x and D^=2y, find the values of x and y.

If the opposite angles of a quadrilateral are supplementary, what can you conclude about the quadrilateral?

In triangle ABC, altitudes BD and CE intersect at H. Prove that quadrilateral AEHD is cyclic.

In cyclic quadrilateral PQRS, PQ^​S=50∘ and QS^R=30∘. Find PS^R and PQ^​R.

Two circles intersect at A and B. A straight line PAQ meets the circles at P and Q. Another straight line RBS meets the circles at R and S. Prove that PR is parallel to QS.

Prove that the exterior angle of a cyclic quadrilateral is equal to the interior opposite angle.

In a cyclic quadrilateral ABCD, the bisector of angle A meets the circle at P and the bisector of angle C meets the circle at Q. Prove that PQ is a diameter of the circle.

A circle is drawn with the hypotenuse of a right-angled triangle as diameter. Prove that the circle passes through the vertex containing the right angle.

ABCD is a cyclic quadrilateral. If AD=BC, prove that the diagonals are equal (AC=BD).