Prove that :
the rhombus , inscribed in a circle is a square.

Prove that the rectangle circumscribing a circle is a square

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

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

Prove that the parallelogram circumscribing a circle is a rhombus.

Prove that the parallelogram circumscribing a circle is a rhombus.

Prove that the parallelogram circumscribing a circle is a Rhombus.

If all the side of a parallelogram touch a circle, show that the parallelogram is a rhombus. OR Prove that a parallelogram circumscribing a circle is a rhombus.

Show that of all the rectangles inscribed in a given circle, the square has the maximum area.

A wire of length l is cut into two parts. One part is bent into a circle and the other into a square. Prove that the sum of the areas of the circle and the square is the least, if the radius of the circle is half of the side of the square.