9.3. Arcs in Circles http://www.ck12.org
9.3 Arcs in Circles
Here you’ll learn the properties of arcs and central angles of circles and how to apply them.
What if the Ferris wheel below had equally spaced seats, such that the central angle were 20◦. How many seats are
there? Why do you think it is important to have equally spaced seats on a Ferris wheel?
If the radius of this Ferris wheel is 25 ft., how far apart are two adjacent seats? Round your answer to the nearest
tenth. The shortest distance between two points is a straight line.
Watch This
MEDIA
Click image to the left for more content.CK-12 Foundation: Chapter9ArcsinCirclesA
MEDIA
Click image to the left for more content.Brightstorm:CentralAngles
Guidance
Acentral angleis the angle formed by two radii of the circle with its vertex at the center of the circle. In the picture
below, the central angle would be^6 BAC. Every central angle divides a circle into twoarcs(anarcis a section of the
circle). In this case the arcs areBĈandBDĈ. Notice the arc above the letters. To label an arc, always use this curve
above the letters. Do not confuseBCandBĈ.
IfDwas not on the circle, we would not be able to tell the difference betweenBĈandBDĈ. There are 360◦in a
circle, where a semicircle is half of a circle, or 180◦.m^6 EF G= 180 ◦, because it is a straight angle, somEHĜ= 180 ◦
andmEJĜ= 180 ◦.
- Semicircle:An arc that measures 180◦.
- Minor Arc:An arc that is less than 180◦.
- Major Arc:An arc that is greater than 180◦.Alwaysuse 3 letters to label a major arc.