In ∆ABC, points A and D are joined where D is a point on BC. E is a point on AC such that BE is perpendicular to AC and BE intersects AD at point X, which is the orthocentre of ∆ABC. F is the mid-point of AB such that CF intersects AD at Y, which is the centroid of ∆ABC, and BE at G. If it is known that, length of YD is half that of the length of XY, then how many of the following statements must be true? I. BC² < AB² + AC² II. Area of ∆XYG = 0.5 × Area of ∆AFY III. AD = BD