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?