Question 1095076
<br>If a parallelogram has one vertex at the center of a circle and the other three vertices on the circle, then two adjacent sides of the parallelogram are the same length; that means the parallelogram is a rhombus.<br>
In fact, the rhombus has to be one with angles of 60 and 120 degrees.<br>
If you have trouble visualizing that (I did!), inscribe a regular hexagon ABCDEF in circle O and draw radii OA, OC, and OE....<br>
So a parallelogram with the specified conditions  has to be a rhombus with angles of 60 and 120 degrees.