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Geometry: Circles

Circles and Polygons

Problems

Problems

Inscription and Circumscription

Certain geometric figures are created by combining circles with other geometric figures, such as polygons. There are two simple ways to unite a circle with a polygon. One is inscription, and the other is circumscription.

When a polygon is inscribed in a circle, it means that each of the vertices of that polygon intersects the circle. When a polygon is circumscribed about a circle, it means that each of the sides of the polygon is tangent to the circle. Below these situations are pictured.

Figure %: A circle being inscribed and circumscribed by a polygon
Above on the left, the hexagon ABCDEF is inscribed in the circle G. On the right, the quadrilateral ABCD is circumscribed about the circle E.

Concentric Circles

One more brief topic to introduce is concentric circles. Concentric circles are circles that have the same center. Just because a circle is inside another circle doesn't mean they are concentric; they must have the same point as their center. Any number of circles can be concentric to one another, provided that they all share a center. Below a few are pictured.

Figure %: Concentric circles

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