In the figure, `P` is the centre of the circle. Prove that: `/_X P Z=2\ (/_X Z Y+\ /_Y X Z)`

In Figure, O is the centre of the circle, prove that /_x=/_y+/_z

In Figure,O is the centre of the circle,prove that /_x=/_y+/_z

If the and and terms of a G.P.are x,y and z,respectively. Prove that x,y,z are in G.P.

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

If x,1, and z are in A.P.and x,2, and z are in G.P.then prove that x, and 4,z are in H.P.

If the m th, n th and p th terms of an AP and GP are equal and are x , y , z , then prove that x^(y-z) . y^(z-x) z^(x-y)=1

If x, y, z,w in are in G.P., prove that (xy-wz)/(y^2-z^2)=(x+z)/y .

If x, y, z be the pth, qth, rth terms respectively both of an A.P. and of a G.P. prove that x^(y-z).y^(z-x).z^(x-y) = 1 .

If a^(x) = b^(y) = c^(z) and a, b, c, are in G.P., prove that x, y, z are in H.P.