Central Angles, Radii, and Chords
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.
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:
