Section 12­1Circles and Arcs.notebook
October 21, 2014
Math 3 ~ Mrs. Naylor
Section 12­1: Circles and Arcs
I CAN...
Prove that all circles are similar G­C­1
Circle: set of all points equidistant from a given point called the center
Center: name of the circle
Diameter: segment that contains the center of the circle with both endpoints on the circle
Radius: segment that has one endpoint at the center and the other endpoint on the circle
Congruent Circles: have congruent radii
Central Angle: an angle whose vertex is at the center of a circle
Section 12­1Circles and Arcs.notebook
October 21, 2014
Semicircle: half of a circle
Minor Arc: smaller than a semicircle
Major Arc: larger than a semicircle
Arc Measure: equal to the measure of its corresponding central angle
Adjacent Arcs: arcs of the same circle that have exactly one point in common
Postulate 19: Arc Addition Postulate
The measure of the arc formed by two adjacent arcs is the sum of the measures of the two arcs
mABC = mAB + mBC
Section 12­1Circles and Arcs.notebook
October 21, 2014
Circumference: the distance around a circle
Theorem 72: Circumference of a Circle
C = 2πr
C = πd
Concentric Circles: coplanar circles that have the same center
Arc Length: a fraction of the circumference
Theorem 73: Arc Length
The length of an arc of a circle is the product of the ratio
measure of the arc and the circumference of the circle
360
length of AB = mAB x 2πr
360
Section 12­1Circles and Arcs.notebook
Naming Arcs
Example 1:
What are the minor arcs of Ο O?
Example 2:
Ο
What are the semicircles of O?
Example 3:
Ο
What are the major arcs of O?
Finding the Measures of Arcs
Example 4:
What is the measure of BC?
Example 5: What is the measure of BD?
Example 6: What is the measure of ABC?
Example 7:
What is the measure of AB?
October 21, 2014
Section 12­1Circles and Arcs.notebook
Finding a Distance
Example 8:
A 2 foot wide circular track for a camera dolly is set up for a movie scene. The two rails of the track form concentric circles. The radius of the inner circle is 8 feet. How much farther does a wheel on the outer rail travel than a wheel on the inner rail of the track in one turn?
Example 9:
A car has a circular turning radius of 16.1 feet. The distance between the two front tires is 4.7 feet. How much farther does a tire on the outside of the turn travel than a tire on the inside?
October 21, 2014