Prove that the parallelogram circumscribing a circle is a rhombus.

Prove that opposites of a quadrilaterial circumscribing a circle subtend supplementary angles at the centre of the circle.

Prove that a cyclic parallelogram is a rectangle.

Write the inverse , converse of 'If a parallelogram is a square , then it is a rhombus.

Write the contrapositive and converse of "If a paralleogram is a square,then it is a rhombus".

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

The lengths of three consecutive sides of a quadrilateral circumscribing a circle are 4 cm, 5 cm, and 7 cm respectively . Determine the length of the fourth side.

Prove that the circle drawn with any side of a rhombus as diameter, passes through the point of intersection of its diagonals.

If the sides of a parallelogram touch a circle, prove that parallelogram is a rhombus.

Diagonal AC of a parallelogram ABCD bisects A. Show that ABCD is a rhombus.