Points N and R both lie on circle O. Line segment RQ is tangent to the circle at point R.

Circle O is shown. Line segments O R and O N are radii. A line is drawn to connects points R and N to form chord R N. Point Q is outside of the circle. Lines are drawn from points R and N to point Q to form an isosceles triangle. The lengths of R N and N Q are congruent. The length of O N is 5 and the length of R Q is 5 StartRoot 3 EndRoot.

What is the perimeter of triangle RON?