1. Advanced Geometry Circles Lesson 1

2. Diameters, radii, and chords are all segments,
Definition – the locus of all points in a plane
equidistant from a given point
A circle is named by
its center point.
Name:
Diameters, radii, and chords are all segments,
lines, or rays.

3. Examples:
Identify each part of the circle below.
Name the circle.
Name a radius of the circle.
Name a diameter of the circle
Name a chord of the circle.

4. Examples:
Circle R has diameters .
and
If ST = 18, find QM. 18
If RN = 2, find QM. 4
If PR = 11, find RT. 11

5. Example:
The diameters of X, Y, and Z are 22
millimeters, 16 millimeters, and 10 millimeters,
respectively. Find EZ.

6. Examples:
Find each measure to the nearest hundredth.
Find C if r = 13 inches.
Find C if d = 6 millimeters.
Find d and r to the nearest hundredth if C = 65.4 feet.

7. Examples:
Find the exact circumference of K.

8. Find the exact circumference of P.
Examples:
Find the exact circumference of P.
9 ft
12 ft

9. Example:
is a diameter of
T. Find m
RTS.

10. Central Angle
Vertex is at the center
Arc
a piece of a circle

11. 2 endpoints, 1 interior point, and
Naming Arcs
Minor Arc
2 endpoints and
an arc symbol
Major Arc
2 endpoints, 1 interior point, and
an arc symbol

12. 2 endpoints, 1 interior point, and
Naming Arcs
Semicircle
2 endpoints, 1 interior point, and
an arc symbol

13. = 90 = 67 = 316 Examples: In P, and are diameters, m NPM = 46, bisects
KPM,
and
. Find each measure.
= 90
= 67
= 316

14. The table below shows the percent of each type
Example:
The table below shows the percent of each type
of bicycle sold in the United States in 2001.
Find the measure of
the central angle
representing each
category.
Type of Bicycle %
Comfort 21
Mountain 37
Youth 26
Hybrid 9
Other 7
75.6º
133.2º
93.6º
32.4º
25.2º
Describe the kind of arc associated with each category.