BdMO National Higher Secondary 2007/2

[BdMO]

Problem 2:
$WZ$ is the diameter of circle with center $O$. $OY=5$, arc $XY$ creates angle $60^{\circ}$ at the center. If $\angle ZYO=60^{\circ}$, then $XY=?$.

[photon]

I think X,Y are on the circumference.
Then OX=OY. So it's a equilateral triangle.
XY=5

[checkmatec4]

If I am not wrong, then the solution is:
Between triangle XOY and OYZ, XO=OY=OZ=5 (radius of the same circle) and <XOY=<OYZ=60 degree.
So, triangle XOY =~ OYZ. So, XY=OZ=5.