Ellipse

Let P(x1,y1) and Q(x2,y2) be two distinct points on the ellipse
‌

x2

9

+‌

y2

4

=1
such that y1>0, and y2>0. Let C denote the circle x2+y2=9, and M be the point (3,0).
Suppose the line x=x1 intersects C at R, and the line x=x2 intersects C at S, such that the y-coordinates of R and S are positive. Let ∠ROM=‌

π

6

and ∠SOM=‌

π

3

, where O denotes the origin (0,0). Let |XY| denote the length of the line segment XY.
Then which of the following statements is (are) TRUE?