If x,y,z are the perpendiculars from the vertices of a triangle ABC on the opposite sides a,b,c respectively, then show that `(bx)/c+(cy)/a+(az)/b=(a^2+b^2+c^2)/(2R)`

The perpendicular from the vertices A, B and C of a triangle ABC on the opposite sides meet at O. If OA=x, OB=y and OC=z, prove that, a/x + b/y + c/z = (abc)/(xyz) .

If x , ya n dz are the distances of incenter from the vertices of the triangle A B C , respectively, then prove that (a b c)/(x y z)=cot(A/2)cot(B/2)cot(C/2)

OX,OY and OZ are the perpendiculars drawn from an internal point O of the Delta ABC on its sides BC,CA and AB respectively. Prove that AZ^(2) + BX^(2) + CY ^(2) = AY^(2) + CX^(2) + BZ^(2)

If a, b, c are In A.P., then show that, (a+2b-c) (2b+c-a)(c+a-b) = 4abc

If the lengths of the sides vec(BC), vec(CA) and vec(AB) of the triangle ABC be a:b:c respectively and the lengths of perpendicular from the circumcenter upon vec(BC), vec(CA) and vec(AB) be x, y, z respectively, then prove that, a/x + b/y + c/z = (abc)/(4xyz) .

In any triangle ABC show that b^2sin2C+c^2sin 2B=abc/R

A, B and C are interior angles of a triangle ABC, then sin ((B + C)/(2)) =

If in a triangle ABC, anglesA, B,C are in A.P, sides a,b,c are In G.P., then a^2,b^2,c^2 are in

If in Delta ABC , the distance of the vertices from the orthocenter are x,y, and z then prove that (a)/(x) + (b)/(y) + (c)/(z) = (abc)/(xyz)

If A, B and C are interior angles of a triangle ABC, then show that sin((B+C)/2) =Cos (A/2) ​