Shope's Theorem

Shope’s Theorem states that if a polygon’s sides and angles meet certain specific conditions—mainly involving the angles adding up in a particular way—then the polygon can be inscribed in a circle. This means all its vertices lie on a common circle, creating a cyclic polygon. The theorem helps identify when a polygon is cyclic based on its angles and side arrangements, which is useful in geometry for solving problems related to circle properties and polygon construction. It’s a way to understand how certain geometric shapes fit perfectly inside circles.