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

If 4 sides of a quadrilateral ABCD are tangents to a circle, then

If the diagonals of a quadrilateral divide each other proportionally, then prove that the quadrilateral is a trapezium.

ABCD is a cyclic quadrilateral. Find the angles of the cyclic quadrilateral.

ABCD is a cyclic quadrilateral. Find the angles of the cyclic quadrilateral.

AC and BD are chord of a circle which bisect each other. Prove that (ii) ABCD is a rectangle.

Given statements in (a) and (b). Identify the statements given below as contrapositive or converse of each other. (b) 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 a quadrilateral bisect each other, then it is a parallelogram.

ABCD is a cyclic quadrilateral. Find the angle A of the cyclic quadrilateral.

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

The equation of the diagonal through the origin of the quadrilateral formed by x=0, y=0 , 3 x+y=1 and 4 x+y=7 is

Prove that a cyclic parallelogram is a rectangle.