##### Like what you saw?

##### Create FREE Account and:

- Watch all FREE content in 21 subjects(388 videos for 23 hours)
- FREE advice on how to get better grades at school from an expert
- Attend and watch FREE live webinar on useful topics

# Circumscribed and Inscribed Circles and Polygons - Concept

###### Brian McCall

###### Brian McCall

**Univ. of Wisconsin**

J.D. Univ. of Wisconsin Law school

Brian was a geometry teacher through the Teach for America program and started the geometry program at his school

A circle is circumscribed about a polygon if the polygon's vertices are on the circle. For triangles, the center of this circle is the circumcenter. A circle is inscribed a polygon if the sides of the polygon are tangential to the circle. For triangles, the center of this circle is the incenter. **Circumscribed and inscribed circles** show up a lot in area problems.

Two terms that get confused in Geometry are the words circumscribed and inscribed. But what's the difference? Well let's take a look at a couple of examples.

This first example we have a triangle that is inside of a circle. Well, the way that we could say this is either the polygon is inscribed in the circle, that's the general way. But since we have a triangle I could say the triangle is inscribed in the circle. Notice that the triangle's within the triangle so that's how you can say it's inscribed. The reverse of that is to say the circle is circumscribed about the polygon. So if you're wondering this is formed by the point of concurrency called the circumcenter which is formed by the three perpendicular bisectors.

Let's look at inscribed. With an inscribed circle, we have the circle that's within the polygon. Notice that here we have a triangle and a circle inside of it, and here we have the quadrilateral with a circle inside of it. So if I look at this quadrilateral, there's two ways that I can describe this picture.

The first is the quadrilateral is circumscribed about the circle. Notice that when we use the word circumscribe we're using about. We could also say that this circle is inscribed inside the quadrilateral. So two different ways to describe the same picture.

Inscribe you should think is within its inside, and whenever you hear the word circumscribing you should be thinking about or outside.

Please enter your name.

Are you sure you want to delete this comment?

###### Brian McCall

B.S. in Chemical Engineering, University of Wisconsin

J.D. University of Wisconsin Law School (magna cum laude)

He doesn't beat around the bush. His straightforward teaching style is effective and his subtle midwestern accent is engaging. There's never a dull moment with him.

so my teacher can't explain this in 5 weeks but I learn this in less than 3 minutes”

its hard to focus when the teacher is really really really goodlooking”

i like how it took you 3 minutes and 8 seconds to accomplish what my teacher couldn't in 3 days”

###### Get Peer Support on User Forum

Peer helping is a great way to learn. Join your peers to ask & answer questions and share ideas.

#### Related Topics

- Constructing the Centroid 15,380 views
- Constructing a Perpendicular at a Point on a Line 11,342 views
- Duplicating a Line Segment 20,619 views
- Duplicating an Angle 14,016 views
- Constructing the Perpendicular Bisector 30,011 views
- Constructing a Perpendicular to a Line 14,140 views
- Constructing an Angle Bisector 23,176 views
- Constructing Parallel Lines 18,144 views
- Constructing Altitudes 23,853 views
- Constructing a Median 13,624 views
- Constructing a Triangle Midsegment 10,747 views
- Point of Concurrency 27,579 views
- Constructing the Incenter 10,353 views
- Constructing the Circumcenter 14,049 views
- Constructing the Orthocenter 24,163 views

## Comments (0)

Please Sign in or Sign up to add your comment.

## ·

Delete