What is an inscribed polygon?

An inscribed polygon is a two-dimensional shape contained entirely within a circle. The points of each corner are on the circumference of the circle. Inscribed polygons have other special geometric properties.

For example, the opposite angles of a four-sided polygon inscribed in a circle are supplementary. This means that when added together, the measure of the angles is 180 degrees. Not all four-sided figures can be inscribed. Parallelograms are impossible to inscribe in a circle. Any circle drawn that touches three of a parallelogram's corners will be too big to touch the forth corner. Polygons that can be inscribed are called cyclic.