Central Angles, Radii, and Chords

Author:
Kim Hager
Topic:
Angles
Image

Warm Up

1) What do you think of when you hear the word "central"? 2) What do you think of when you hear the word "inscribed"? 3) What does the word "circumnavigate" mean?

Identifying Features of a Circle

Vocab Review

A radius (pl: radii) is a segment with one endpoint at the center of the circle and one endpoint on the circle. A chord is a segment with both endpoints on the circle. An arc is a set of points that lie on a circle. An angle is subtended by an arc when that arc's endpoints are the same as the angle's endpoints. An arc's measurement is then the same as the measurement of the central angle that intercepts it. Minor arcs are less than 180 degrees and labeled with two points. Major arcs are greater than 180 degrees and labeled with three points. An arc with exactly 180 degrees is a semicircle.

Radii and Chords

Given the applet above, name two radii of the circle.

Given the applet above, name one chord of the circle.

Check all that apply

How can you make a second chord without drawing any new segments?

What do you notice as you move the points on the circle?

Using the applet as a guide, what do you think a central angle is?

What do you wonder about as you look at and manipulate the applet?

A Note about Arcs

The arc's measurement is the same as the measurement of the central angle. Arc length, however, is measured in the same units as the circle's circumference. In this lesson, we'll be talking about the measurement of arcs.

Using the applet above, if m<BAC is 120 degrees, what is the measure of arc BC?

Look again at this picture:

Look again at this picture:
Can you find a central angle? What can you say about the central angle in this picture? If you were to describe the visible radii of this ferris wheel to someone, how would you describe them?

When you've checked your answers and sharing with a classmate but before you go onto the next worksheet, please complete one Khan Academy module.