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Math 102: College Mathematics14 chapters | 108 lessons

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Lesson Transcript

Instructor:
*Jeff Calareso*

Jeff teaches high school English, math and other subjects. He has a master's degree in writing and literature.

Circles are fundamental to everything we do. But, did you know they're much more than just round shapes? In this lesson, we'll look at the various parts of circles and how they all relate.

Before there were circles, the world was a very sad place.

When you ordered a pizza, the delivery guy took forever to get to you.

Then the pizza slices didn't always have helpful handles.

And pepperoni? There was no pepperoni. There was only saber tooth tiger sausage, which was kind of gamey.

Fortunately, we now have circles. And, while you may not think of circles as much more than those round shapes of pizza and wheels, they actually contain many interesting parts and properties. Let's take a closer look.

First and foremost, let's define a circle. A **circle** is the set of all points that are a fixed distance from a center point.

Every circle starts with a center. If you had a compass, you'd stick the point in that center and then you could draw an infinite number of dots that are all the same distance from that center. Those dots would comprise your circle.

The distance from the center to any point on the circle is called the **radius**. In your pizza, it's the length of your slice.

If we consider the distance across the circle, passing through the center, that's the **diameter**. When you use your awesome pizza slicer (which is itself a circle) to slice up your pie, you're cutting diameters. Well, if you can get it through the center you are. I sometimes navigate around pepperoni slices in order to achieve equal meat distribution across all slices. I'm not proud of that.

So, how do you remember which line is the radius and which is the diameter? Well, the word radius is shorter than the word diameter, just like the radius is shorter than the diameter.

Then there's the **circumference**. This is the distance around the circle. And, stick with me here, the word circumference is the longest in letters of these three terms, and it is the longest part. You could also think about circumnavigating the globe - you're going around the planet.

Those are the most critical parts of a circle, but there are more things you should know.

We've been focusing on pizza, but there's another type of pie you've probably heard mentioned. That's **pi** without an 'e.' This is the circumference of a circle divided by the diameter, or 3.14. It doesn't matter how big or small your circle is, the circumference divided by the diameter will always be 3.14. Actually, it's 3.14159265358979..., well, it goes on forever. But, we usually just abbreviate it 3.14 or use a symbol.

There are also other pieces of circles. For example, if you draw a line connecting two points on a circle, it's called a **chord**. This chord is an example of someone who doesn't really get how to slice a pizza. And that piece formed by the chord? That's a segment. That makes sense - it's a segment of a pizza.

If the line doesn't stop at the edge of a circle, but goes on beyond it, it's a secant. That's your runaway pizza slicer.

If you go to slice your pizza and totally miss, but just touch the edge, then you should probably slow down. But, you also just cut a **tangent** into your table, which is a line that touches, but doesn't cross, a circle.

Maybe you've heard tangent used in other contexts. For example, you might say that my opinion on equal pepperoni distribution is tangentially related to this lesson. It's connected, but barely.

Finally, there's a name for a part of the circumference of a circle. That's called an **arc**. If we can talk about something other than pizza for a moment, I like to think of an arch, like the one in St. Louis. An arch is a curved shape that's like part of a circle, and an arc is very similar.

But, back to pizza. When you take an arc and connect its ends to the center, you have a sector. That's your traditional pizza slice. Depending on the length of your arc, your sector may or may not have as much pepperoni as everyone else's. You're at the mercy of the person slicing it.

In summary, we looked at the many properties of the **circle**, or the shape created by the set of all points a fixed distance from a center point.

There's the **radius**, which is the distance from the center to any point on the circle, and the **diameter**, which is the distance across the circle, passing through the center. If we're looking at the distance around the circle, that's the **circumference**.

We learned that **pi** is the circumference divided by the diameter, or 3.14.

Then, there were other fun parts, like the chord, arc, and tangent. Finally, may all your geometry lessons require you to get pizza to study.

Following this lesson, you'll be able to:

- Define circle
- Explain what the radius, diameter and circumference of a circle are
- Define pi and identify what number is typically used to represent pi
- Describe chord, arc, tangent and secant in relation to circles

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Math 102: College Mathematics14 chapters | 108 lessons

- Go to Logic

- Go to Sets

- Properties of Shapes: Rectangles, Squares and Rhombuses 5:46
- Properties of Shapes: Triangles 5:09
- Perimeter of Triangles and Rectangles 8:54
- Area of Triangles and Rectangles 5:43
- Circles: Area and Circumference 8:21
- The Pythagorean Theorem: Practice and Application 7:33
- How to Identify Similar Triangles 7:23
- Applications of Similar Triangles 6:23
- Parallel, Perpendicular and Transverse Lines 6:06
- Types of Angles: Vertical, Corresponding, Alternate Interior & Others 10:28
- Angles and Triangles: Practice Problems 7:43
- Properties of Shapes: Circles 4:45
- Go to Geometry

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