Prove that the bisectors of the four angles of quadrilateral produce jointly a cyclic quadrilateral.

Prove that the opposite angles of a cyclic quadrilateral are suplemenary.

If the degree measure of the sum of any two opposite angles of a quadrilateral is ………….. ,then it is a cyclic quadrilateral.

Answer any one question : Prove that the quadrilateral foemed by the internal bisectors of the four angles of a quadrilateral is cyclic.

The opposite angles of a cyclic quadrilateral are ……………

Prove that opposite angles of a cyclic quadrilateral are supplementary

Prove that the internal bisector of any angle of a cyclic quadrilateral and the external bisector of its opposite angle intersect each other on the circumference of the circle.

The area of any cyclic quadrilateral ABCD is given by A^(2) = (s -a) (s-b) (s-c) (s-d) , where 2s = a + b ++ c + d, a, b, c and d are the sides of the quadrilateral Now consider a cyclic quadrilateral ABCD of area 1 sq. unit and answer the following question The minium perimeter of the quadrilateral is

The area of any cyclic quadrilateral ABCD is given by A^(2) = (s -a) (s-b) (s-c) (s-d) , where 2s = a + b ++ c + d, a, b, c and d are the sides of the quadrilateral Now consider a cyclic quadrilateral ABCD of area 1 sq. unit and answer the following question When the perimeter is minimum, the quadrilateral is necessarily

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.