If in ` A B C ,` the distances of the vertices from the orthocentre are x, y, and z, then prove that `a/x+b/y+c/z=(a b c)/(x y z)`

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)

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

If the foot of the perpendicular from the origin to plane is P(a ,b ,c) , the equation of the plane is a. x/a=y/b=z/c=3 b. a x+b y+c z=3 c. a x+b y+c z=a^(2)+b^2+c^2 d. a x+b y+c z=a+b+c

In the adjacent figure, find the value of x, y, z and a, b, c.

If x,y and z are in A.P ax,by and cz in G.P and a, b, c in H.P then prove that x/z+z/x=a/c+c/a

The minimum value of P=b c x+c a y+a b z , when x y z=a b c , is

If x ,ya n dz are in A.P., a x ,b y ,a n dc z in G.P. and a ,b ,c in H.P. then prove that x/z+z/x=a/c+c/a .

If a, b, c are in geometric progression, and if a^(1/x)=b^(1/y)=c^(1/z) , then prove that x, y, z are in arithmetic progression.

If a^x=b ,b^y=c ,c^z=a , then find the value of x y zdot

A plane passes through a fixed point (a ,b ,c)dot Show that the locus of the foot of the perpendicular to it from the origin is the sphere x^2+y^2+z^2-a x-b y-c z=0.