If `S=a+b+c` then prove that `(S)/(S-a)+(S)/(S-b)+(S)/(S-c) gt (9)/(2)` where a,b & c are distinct positive reals.

If c^(2) = a^(2) + b^(2) , then prove that 4s (s - a) (s - b) (s - c) = a^(2) b^(2)

If S _(r) denote the sum of first 'r' terms of a non constaint A.P. and (S_(a ))/(a ^(2)) =(S_(b))/(b ^(2))=c, where a,b,c are distinct then S_(c) =

The point P(a,b), Q(c,d), R(a,d) and S(c,b) , where a,b,c ,d are distinct real numbers, are

In Delta ABC, a^(2)(s-a)+b^(2)(s-b)+c^(2)(s-c)=

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.

If c^2 = a^2 + b^2, 2s = a + b + c , then 4s(s-a) (s - b)(s-c)

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

If in Delta ABC, (a -b) (s-c) = (b -c) (s-a) , prove that r_(1), r_(2), r_(3) are in A.P.

If C is the centre of a hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 , S, S its foci and P a point on it. Prove tha SP. S'P =CP^2-a^2+b^2

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