Final answer:
A parallelogram inscribed in a circle is a special kind of parallelogram; it must be a rectangle because the only parallelogram that can have all corners touch the circle is a rectangle.
Step-by-step explanation:
When considering the type of parallelogram that can be inscribed in a circle, it's important to recall the properties of a circle and an ellipse. In a circle, the center is equidistant to all points on the circumference. On the other hand, an ellipse has two focal points, or foci, and the sum of the distances from these foci to any point on the ellipse remains constant. This characteristic is key to drawing an ellipse using a loop of string.
However, a parallelogram inscribed in a circle is a very special case. It's not just any parallelogram; it has to be a rectangle because the only type of parallelogram that can have all four corners touching the circle, which is called a circumscribed circle or circumcircle, is a rectangle. This is due to the fact that the opposite angles of a parallelogram inscribed in a circle must be supplementary, and the only parallelogram with consecutive supplementary angles is a rectangle.