Notice, also: in the case of a right triangle, the second image, the hypotenuse of the triangle is the diameter of the circumscribed circle. Notice that, when one angle is particularly obtuse, close to 180°, the size difference between the circumscribe circle and the inscribed circle becomes quite large. Here’s a small gallery of triangles, each one both inscribed in one circle and circumscribing another circle. That “universal dual membership” is true for no other higher order polygons -– it’s only true for triangles. Every single possible triangle can both be inscribed in one circle and circumscribe another circle. In both cases, the outer shape circumscribes, and the inner shape is inscribed.Īs is the case repeatedly in discussions of polygons, triangles are a special case in the discussion of inscribed & circumscribed. Now, the pentagon is circumscribed around the circle, and the circle is inscribed in the pentagon. Notice, now, that each side of this irregular pentagon is tangent to the circle. Here’s another diagram with the polygon on the outside. The word “inscribed” describes the inside shape, and the word “circumscribed” describes the outside shape. We can also say: the circle circumscribes the pentagon. In this diagram, the irregular pentagon ABCDE is inscribed in the circle, and the circle is circumscribed around the pentagon. When a polygon is “inside” a circle, every vertex must lie on the circle: One more sophisticated type of geometric diagram involves polygons “inside” circles or circles “inside” polygons.
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