Prove that a cyclic rhombus is a square

Prove that a cyclic parallelogram is a rectangle.

Prove that the area of a rhombus is equal to half of the product of the diagonals.

State whether the statements are True or False. (v) Every rhombus is a square ( )

Prove that if A is a square matrix then ,(i) (A+A') is a symmetric metrix. (ii) (A-A') is a skew symmetric matrix.

Prove that three times the square of any side of an equilateral triangle is equal to four times the square of the altitude.

ABCD is a square. E, F, G and H are the mid points of AB, BC, CD and DA respectively. Such that AE = BF = CG = DH . Prove that EFGH is a square.

Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals.

Prove that the sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of its sides.

In an equilateral triangle, prove that three times the square of one side is equal to four times the square of one of its altitude.

Work done in the cyclic process shown in figure is :-