What is the right course of action?

You answered correctly. In this situation, the cyclist coming from the right has priority because of the "right before left" rule at intersections without priority signs. This means you must let the cyclist go first. After the cyclist has passed, you may proceed before the motorcycle since you are going straight and the motorcycle is turning left, which must yield to oncoming traffic. The answer that the cyclist must allow you to pass is incorrect, as you do not have priority over the cyclist coming from the right. Remember: always yield to vehicles approaching from the right at intersections without traffic signs.