If we can draw a circle, which touches four sides of a parrallellogram, then prove that the parallelogram is a rhombus.

Prove that if both pairs of opposite sides of a quadrilateral are equal, then it is a parallelogram.

If a circle can be drwan by touching the sides of parallelogram inside it will be a rhombus. Prove. . Draw the figure AP=AS,BP=BQ,DR=DS,CR=CQ. Using these equations prove the statements given as the 11th point in the basic concepts. 2xxAB = 2xxAD

In the figure a circle touches the sides of ? ABC at P, Q, R. If AB=AC then prove that BR=CR Why is AP=AQ?

Prove that a parallelogram which is not a rectangle is not cyclic.

In the figure ABCD iś a parallelogram. dotP, Q, R and S are the midpoint of the sides of the parallelogram. Prove that P Q=R S and Q R=P S .

Find the area of a parallelogram for which the vectors 2i+j,3i+j+4k are adjacent sides.

In the picture below, two vertices of a parallelogram are joined to the mid points of two sides. Prove that these lines divides the diagonal in the picture into three equal parts. .