Prove that the parallelogram circumscibing a circle is a rhombus.

Prove that the parallelogram circumscribed about a circle is only a rhombus.

Prove that a cyclic parallelogram must be a rectangle.

Prove that an angle inscribed in a semi-circle is a right angle using vector method.

Prove that ,the greatest rectangle inscribed in a given circle is a square.

If diagonals of a parallelogram bisect each other, prove that its a rhombus.

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

Prove that the area of the parallelogram produced by joining the mid-points of the sides of a quadrilateral taken in order is half the area of the quadrilateral.

Prove that if the two diagonals of any parallelogram intersect each other orthogonally, then the parallelogram is a rhombus.

Using dot product of vectors, prove that a parallelogram, whose diagonals are equal, is a rectangle

Prove that "The greatest chord of circle is its diameter".