In a cyclic quadrilateral ABCD, prove that `tan ^(2)""(B)/(2)=((s-a)(s-b))/((s-c)(s-d)),a,b,c, and d` being the lengths of sides ABC, CD and DA respectively and s is semi-perimeter of quadrilateral.

In a cyclic quadrilateral A B C D , if /_A=3 /_C . Find /_A

If any quadrilateral ABCD, prove that "sin"(A+B)+sin(C+D)=0 "cos"(A+B)=cos(C+D)

If any quadrilateral ABCD, prove that "sin"(A+B)+sin(C+D)=0 "cos"(A+B)=cos(C+D)

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

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 minimum value of the sum of the lenghts of diagonals is

ABCD is a rhombus and P, Q, R and S are wthe mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rectangle.

If A B C D is a cyclic quadrilateral in which A D || B C . Prove that /_B=/_C

ABCD is a rectangle and P, Q, R and S are mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rhombus.

Prove that : (r_1)/((s-b)(s-c))+(r_2)/((s-c)(s-a))+(r_3)/((s-a)(s-b))=3/r