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# 9.8: Inscribed and Circumscribed Polygons

Difficulty Level: At Grade Created by: CK-12

## Learning Objectives

• Recognize characteristics of inscribed polygons formed by chords and circumscribed polygons formed by tangent segments.

## Inscribed and Circumscribed Polygons

• A convex polygon whose vertices all touch a circle is said to be an inscribed polygon.
• A convex polygon whose sides all touch a circle is said to be a circumscribed polygon.

The figures below show examples of inscribed and circumscribed polygons:

• \begin{align*}A(n)\end{align*} _____________________________ polygon looks like it is inside a circle.
• \begin{align*}A(n)\end{align*} _____________________________ polygon looks like it is outside a circle.
• When all of the ________________________ of a convex polygon touch a circle, the polygon is inscribed.
• When all of the ________________________ of a convex polygon touch a circle, the polygon is circumscribed.

1. Which type of polygon, inscribed or circumscribed, has sides that are chords of the circle?

\begin{align*}{\;}\end{align*}

\begin{align*}{\;}\end{align*}

\begin{align*}{\;}\end{align*}

\begin{align*}{\;}\end{align*}

2. Which type of polygon, inscribed or circumscribed, has sides that are tangents of the circle?

\begin{align*}{\;}\end{align*}

\begin{align*}{\;}\end{align*}

\begin{align*}{\;}\end{align*}

\begin{align*}{\;}\end{align*}

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