Draw a point B, then draw any two other points D and E. The rays BD and BE are essentially arrows that both start at B and pass through D and E, respectively. See the attached sketch. Note that the points D and E need not lie on a circle like the dotted one in the sketch; they can be placed anywhere along the ray.
Then:
• (I) is sometimes true. Rays can be parallel as long as they are collinear, meaning the three points B, D, and E would need to lie on the same line. (The first sketch shows one example)
• (II) is always true.
• (III) is sometimes true, if the angle the two rays form is a right angle. (The second sketch shows one example)
• (IV) is never true, because B would have to lie on the circle itself. The center does not.
Without knowing what Damiana's/Valeria's drawing looks like, the most we can do is rule out C and D.
