Incircles of Polygons
A circle is inscribed in a polygon if it is tangent to each of the sides of the polygon. Such a circle is called an "incircle." Most polygons do not have incircles, but regular polygons do. We can construct a nonregular polygon that has an incircle by choosing points of tangency on the circle and then constructing the tangent lines whose intersections are the vertices of the polygon. For example, we could construct a nonregular pentagon with an incircle by randomly choosing 5 points on the circumference of the circle, not all on the same semicircle, and constructing tangents at these points:
The resulting pentagon has the given circle as its incircle:
Content ©2008. All Rights Reserved.
Date last modified: May 8, 2009.