Prove that the parallelogram circumscribing a circle is a rhombus.

Prove that a cyclic parallelogram is a rectangle.

Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.

Prove that the centre of the circle circumscribing the cyclic rectangle ABCD is the point of intersection of its diaognsls.

Prove that the parallelogram formed by the lines x/a+y/b=1,x/b+y/a=1,x/a+y/b=2 and x/b+y/a=2 is a rhombus.

If the diagonals of a parallelogram are perpendicular, then it is a rhombus.

Diagonal AC of a parallelogram ABCD bisects angleA show that ABCD is a rhombus.

Prove that, of all the parallelograms of given sides, the parallelogram, which is recatangle has the greatest area.

If I_n is the area of n-s i d e d regular polygon inscribed in a circle of unit radius and O_n be the area of the polygon circumscribing the given circle, prove that I_n=(O_n)/2(sqrt(1+((2I_n)/n)^2))