(a) Solve the equation `sqrt(6-4x-x^2)=x+4` OR (b) Prove that in any `DeltaABC,Delta=sqrt(((s-a)(s-b))/(s(s-c)))`, where s is the semi - perimeter of `DeltaABC`?

In a triangleABC , sqrt[{(s-a)(s-b)}/{s(s-c)}] is:

IF in Delta ABC , sin A/2 sin C /2 =sin B/2 and 2s is the perimeter of the triangle then s is

Prove that the minimum value of ((a+x)(b+x))/((c+x))a ,b > c ,x >-c is (sqrt(a-c)+sqrt(b-c))^2

In A B C , show that a^2(s-a)+b^2(s-b)+c^(2)(s-c))=4R (1+r sin (A/2)sin( B/2)sin( C/2))

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

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

In DeltaABC , the incircle touches the sides BC, CA and AB, respectively, at D, E,and F. If the radius of the incircle is 4 units and BD, CE, and AF are consecutive integers, then the value of s, where s is a semi-perimeter of triangle, is ______

If A + B + C = 2s, then prove that sin (s - A) sin (s - B) + sin s. sin (s - C) = sin A sin B .