Verify area of triangle is (i) abc/4R (ii) 2 R^2 SinA sinB sinC

Verify area of triangle is ( i ) 1/2 bc sin A (ii) Herons Formula (iii) 1/2(a+b+c)r

Prove that the area of triangle ABC= 1/2 ac sinB= 1/2 ab sinC= 1/2 bc sinA

If the area of the triangle ABC is a^(2)-(b-c)^(2), then its circumradius R=

If the area of the triangle ABC is a^(2)-(b-c)^(2) then its circumradius R is

If P is the circumcentre of an acute angled triangle ABC with circumredius R. D is the midpoint of BC. Show that the perimetre of triangleABC = 2R(sinA + sinB + sinC) .

If A,B,C, are the angles of a triangle such that cot(A/2)=3tan(C/2), then sinA ,sinB ,sinC are in (a)AdotPdot (b) GdotPdot (c) HdotPdot (d) none of these

If A,B and C are the angles of a triangle and |{:(1,1,1),(1+sinA,1+sinB,1+sinC),(sinA+sin^(2)A,sinB+sin^(2)B,sinC+sin^(2)C):}| =0 then prove that Delta ABC must be isoceles.