If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, prove that it is a rectangle.

If diagonals of a quadrilateral bisect each other at right angles, then it is a :

If bisectors of opposiste angles of a cyclic quadrilateral ABCD intersect the circle, circumscribing it at the points P and Q, prove that PQ is a diameter of the circle.

The quadrilateral formed by joining the mid-points of the sides of a quadrilateral PQRS, taken in order, is a rectangle, if

Prove that if the diagonals of a quadrilateral bisect each other at right angles, then the quadrilateral is a rhombus.

If the sides of a cyclic quadrilateral are 3,3,4,4, show that a circle be inscribed in it.

If each diagonal of a quadrilateral separated it into two triangles of equal area, then show that quadrilateral is a parallelogram.

Name the quadrilaterals whose diagonals. are equal

ABCD is a cyclic quadrilateral (see Fig.) Find the angles of the cyclic quadrilateral. .

ABCD is a cyclic quadrilateral (see Fig.). Find the angles of the cyclic quadrilateral.