In the given figure, if x + y = w + z, then prove that AOB is a line.

If z=z_0+A( bar z -( bar z _0)), w h e r eA is a constant, then prove that locus of z is a straight line.

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)

Refer to the given figure and identify X, Y and Z in it.

In the given figure three lines bar(AB) , bar(CD) and bar(EF) intersecting at O. Find the values of x, y and z it is being given that x : y : z = 2 : 3 : 5

If x + y + z = xyz, then prove that (2x)/(1- x^(2)) + (2y)/(1 - y^(2)) + (2z)/(1 - z^(2)) = (2x)/(1 - x^(2))cdot (2y)/(1 - y^(2))cdot (2z)/( 1- z^(2)) .

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

Identify the given figure and select the correct option representing X, Y and Z.

If w(x,y) = xy + sin(xy) , then prove that (del^(2) w)/(del y del x) = (del^(2) w)/(del x del y)

Points A( vec a),B( vec b),C( vec c)a n dD( vec d) are relates as x vec a+y vec b+z vec c+w vec d=0 and x+y+z+w=0,w h e r ex ,y ,z ,a n dw are scalars (sum of any two of x ,y ,zn a dw is not zero). Prove that if A ,B ,Ca n dD are concylic, then |x y|| vec a- vec b|^2=|w z|| vec c- vec d|^2dot