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
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.
Stuck on a Math Problem?
Ask Genie for a step-by-step solution
Please enter your name.
Are you sure you want to delete this comment?
- Constructing the Centroid 15,571 views
- Constructing a Perpendicular at a Point on a Line 11,567 views
- Duplicating a Line Segment 20,849 views
- Duplicating an Angle 14,170 views
- Constructing the Perpendicular Bisector 30,301 views
- Constructing a Perpendicular to a Line 14,291 views
- Constructing an Angle Bisector 23,354 views
- Constructing Parallel Lines 18,347 views
- Constructing Altitudes 24,388 views
- Constructing a Median 13,816 views
- Constructing a Triangle Midsegment 10,867 views
- Point of Concurrency 28,063 views
- Constructing the Incenter 10,468 views
- Constructing the Circumcenter 14,205 views
- Constructing the Orthocenter 24,433 views