1. Chapter 9 Section 1
Exploring Circles

2. Vocabulary
Circle- The set of all points in a plane that are a given distances from a given point in that plane.
Center- The given point is the center of the circle.
Radius- A segment that has one endpoint at the center of the circle and the other endpoint in the circle.
Chords- A segment that has its endpoints on the circle.
Diameter- A chord that contains the center of the circle. r

3. Vocabulary cont. Circumference- The distance around the circle.
Π(pi)- The ratio of the circumference of a circle to its diameter.
Circumference of a Circle-
C = 2πr
C = dπ

4. Example 1) The size of a bicycle is determined by the diameter of the wheel. So, a 26-inch bicycle has a wheel with a 26-inch diameter. What is the length of a spoke of a 26-inch bicycle?
The spoke is half the length of the diameter so the spoke would be the length of the radius.
d = 2r
26 = 2r
13 = r
Example 2) The size of a bicycle is determined by the diameter of the wheel. So, a 36-inch bicycle has a wheel with a 36-inch diameter. What is the length of a spoke of a 36-inch bicycle?
The spoke is half the length of the diameter so the spoke would be the length of the radius.
d = 2r
36 = 2r
18 = r

5. Example 3) The radius, diameter, or circumference of a circle is given
Example 3) The radius, diameter, or circumference of a circle is given. Find the other measures to the nearest tenth.
r = 5, d = ?, C = ?
d = 2r
d = 2(5)
d = 10
d = 26.8, r = ?, C = ?
26.8 = 2r
13.4 = r
C) C = 136.9, d = ?, r = ?
C = 2πr
136.9 = 2πr
68.45 = πr
21.8 = r
r = x/6, d = ?, C = ?
d = 2r
d = 2(x/6)
d = x/3
d = 2x, r = ?, C = ?
2x = 2r
x = r
C = 2368, d = ?, r = ?
C = 2πr
2368 = 2πr
1184 = πr
376.9 = r
C = 2πr
C = 2π(5)
C = 10π
C = 2πr
C = 2π(x/3)
C = (2xπ)/3
C = 2πr
C = 2π(13.4)
C = 26.8π
C = 2πr
C = 2π(x)
C = 2πx
d = 2r
d = 2(21.8)
d = 43.6
d = 2r
d = 2(376.9)
d = 753.8

6. Example 3) Refer to the figure to answer the questions.D A
Example 3) Refer to the figure to answer the questions.
Name the center of the circle. M
Name a chord that is also a diameter. RI
If MD = 5, find RI.
d = 2r
d = 2(5)
d = 10
Is MI a chord of the circle? Explain.
No, both the endpoints have to be on the circle for it to be a chord. R M I S U

7. Example 4) Refer to the figure to answer the questions.D A
Example 4) Refer to the figure to answer the questions.
Is MA congruent to MI? Explain.
Yes; they are both radii of the circle and all the radii are congruent.
Name four radii of the circle.
RM, AM, DM, and IM
If RI = 11.8, find MA.
d = 2r
11.8 = 2r
5.9 = r
Is RI > SU? Explain.
Yes, RI is a diameter and the diameter is the longest chord. R M I S U

8. Example 5) Find the exact circumference of the circle.
Since the side of the square is 8 cm, the diameter of the circle is also 8 cm.
C = dπ
C = 8π
Example 6) Find the exact circumference of the circle.
Since we have a right triangle we can find the diameter using the Pythagorean Theorem.
a2 + b2 = c2
= c2
= c2
169 = c2
13 = c
8 cm M
5 cm M
12 cm
So the diameter is 13 cm.
C = dπ
C = 13π