In this edition we will learn about inscribed and circumscribed circles and what their differences are. Circles can be placed inside a polygon or outside a polygon.

__Inscribed circles__

When a circle is placed inside a polygon, we say that the circle is inscribed in the polygon.

An example of a circle inscribed in a triangle is show below.

Notice how each side of the triangle is tangent to the circle at exactly one point.

Notice also that there are 3 points of tangency for the triangle since there are 3 sides and 4 points of tangency for a square since there are 4 sides. When a circle is inscribed in a polygon with n sides, there will be n points of tangency.

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__Circumscribed Circles__

When a circle is placed outside a polygon and each vertex of the polygon lies on the circle, we say that the circle is circumscribed about the polygon. An examples of a circle circumscribed about a square is shown below.

Notice how each vertex of the square lies on the circle. Notice also that there are 4 points that lie on the circle for the square since there are 4 vertices for the square.

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