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)`

In any triangle ABC ,the distance of the orthocentre from the vertices A, B,C are in the ratio

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)

Findthe distance of P(a,b,c) from x,y and z-axes.

If a^x=b ,\ b^y=c\ a n d\ c^z=a , prove that x y z=1

Given x=cy+bz,y=az+cx and z=bx+ay, then prove a^(2) +b^(2) +c^(2) +2abc =1.

If x,y,z are respectively perpendiculars from the circumcentre on the sides of the DeltaABC , the value of a/x+b/y+c/z-(abc)/(4xyz)=

If H is the orthocenter of DeltaABC and if AH = x, BH = y, CH = z , then a/x+b/y+c/z=

If a^x=b^y=c^z\ a n d\ b^2=a c , prove that y=(2x z)/(x+z)

If y^2=x z and a^x=b^y=c^z , then prove that (log)_ab=(log)_bc

If a,b and c are A.P. whereas x,y and z are in G.P. : Prove that : x^(b-c)*y^(c-a)*z^(a-b)=1 .