Let a, b, c be the sides of a triangle & `Delta` its area. Prove that `a^2+b^2+c^2>=4sqrt(3)Delta`, , and find when does equality hold?

Let a, b, c be sides of a triangle ABC and Delta denotes its area . If a=2, Delta=sqrt(3) and a cosC+sqrt(3) a sinC-b-c=0 , then find the value of (b+c) . (symbols used have usual meaning in DeltaABC ).

Let a, b, c be the sides of a triangle and let A, B, C be the respective angles. If b+c=3a, then find the value of the ratio cos((B-C)/2)/cos((B+C)/2)

If a is the smallest side of a triangle and a,b,c are in A.P. prove that "cos" A=(4c-3b)/(2c)

Let alt=blt=c be the lengths of the sides of a triangle. If a^2+b^2< c^2, then prove that angle C is obtuse .

If Delta is the area of a triangle with side lengths a,b,c, then show that as Delta<=(1)/(4)sqrt((a+b+c)abc Also,show that the ) equality occurs in the above inequality if and only if a=b=c.

In an equilateral triangle with side a, prove that area =(sqrt(3))/(4)a^(2)

Let alt=blt=c be the lengths of the sides of a triangle. If a^2+b^2 < c^2, then prove that triangle is obtuse angled .

Let alt=blt=c be the lengths of the sides of a triangle. If a^2+b^2 < c^2, then prove that triangle is obtuse angled .