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

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

If each pair of opposite sides of a quadrilateral is equal, then prove that it is a parallelogram.

The measures of two angles of a cyclic quadrilateral are 40^(@) and 110^(@) Then, the measures of other two angles of the quadrilateral are ..........

The two adjacent sides of a cyclic quadrilateral are 2a n d5 and the angle between them is 60^0dot If the area of the quadrilateral is 4sqrt(3) , find the remaining two sides.

Given statements in a and b. Identify the statements given below as contrapositive or converse of each other. If a quadrilateral is a parallelogram, then its diagonals bisect each other. (i) If the diagonals of a quadrilateral do not bisect each other, then the quadrilateral is not a parallelogram (ii) If the diagonals of the quadrilateral bisect each other then it is a parallelogram.

Prove that a cyclic parallelogram is a rectangle.

Show that if the diagonals of a quadrilateral are equal and bisects each other at right angles, then it is a square.

Let S be the square of unit area. Consider any quadrilateral which has one vertex on each side of S. If a, b, c and d denote the lengths of the sides of the quadrilateral, prove that 2 le a^(2)+b^(2)+c^(2)+d^(2)le 4 .

If two intersecting chords of a circle make equal angles with the diameter passing through their point of intersection, prove that the chords are equal.