# Regular Polygon

__Introduction__

It is often necessary to determine the dimensions of a regular polygon inscribed in or circumscribed about a given circle, or to determine the size of a circle that can be inscribed in or circumscribed about a given polygon. Such problems are readily solved by trigonometry and some of them may be solved by geometry. One practical application of polygons is gears.

__Regular Polygon__

A plane figure bounded by a number of straight lines is called a **polygon**. A **regular polygon** is one in which all sides and all internal angles are equal. A regular polygon has a point $$O$$ inside it called its **center**, which is equidistant from all its vertices and sides. A **convex polygon** is one in which no angle is greater than two right angles, i.e. its has no reflex or re-entrant angle (regular polygons are convex polygons). From the above definitions, triangles and quadrilaterals are also polygons but generally we define a polygon as a figure bounded by more than four straight lines. The sum of the bounding sides of the polygon is called the **perimeter** of the polygon.