Honors Geometry
9.2 Notes
Name_____________________________
Introduction to Circles
Area of a circle (mathematicsonline YouTube channel)
Circumference of a circle
Arc – made up of two points on the circle and all of the points needed to connect those two
points with a single path.
Measure of an arc – is equivalent to the number of degrees it occupies
Length of an arc – a fraction of the circle’s circumference. Length does not equal measure!
Sector – a region bounded by two radii and an arc of the circle.
Area of a sector – a fraction of the circle’s area
Honors Geometry
9.2 Notes
Name_____________________________
G
Examples
N
1. In circle T, the mNR  50 and mGR  90 . The area of the circle is 36 .
R
T
a. Find mGN 40 degrees
b. Find the length of GN
Fraction of circle’s circumference
C = 2*pi*r * (40/360)
A = pi * r * r So the radius is 6
Plug in 6 and you get 12 pi/9 or 4/3 pi
K
2. Find the area of the sector KMS if the radius of circle M is 3
M
and the mKS  130
pi r squared * (130/360)
S
pi * 9 * (13/36)
117 pi/36 units squared
3. If you were to look ahead to Chapter 10, you would discover that the measure of an inscribed
angle is half the measure of its intercepted arc. Use this information to find the measure of
inscribed  MAT .
M
Angle = ½ arc
4x = ½ (6x + 22)
T
x = 11
A