Circles

Advanced GeometryCircles

Lesson 1

A circle is named by its center point.

PName:

Diameters, radii, and chords are all segments,lines, or rays.

Definition – the locus of all points in a plane equidistant from a given point

Examples: Identify each part of the circle below.

Name the circle.

Name a radius of the circle.

Name a chord of the circle.

Name a diameter of the circle

E

, , ,AE BE EC or ED

, , ,AB AC AD or BD

AC or BD

STQMExamples: Circle R has diameters and .

If PR = 11, find RT.

If ST = 18, find QM.

If RN = 2, find QM.

18

4

11

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

Examples: Find each measure to the nearest hundredth.

Find d and r to the nearest hundredth if C = 65.4 feet.

Find C if r = 13 inches.

Find C if d = 6 millimeters.

3 2

Examples: Find the exact circumference of K.

Examples: Find the exact circumference of P.

12 ft

9 ft

RV Example:

is a diameter of T. Find m RTS.

Central AngleVertex is at the center

Arca piece of a circle

is a central angleACB

Minor Arc

Major Arc

Naming Arcs

2 endpoints and an arc symbol

,DE ,EG ,GF ,FD DG

2 endpoints, 1 interior point, and

an arc symbol

DEF ,or DGFEGD ,or EFD

GFDFDG ,or FEG

Semicircle

Naming Arcs

2 endpoints, 1 interior point, and

an arc symbol

EGFEDF

Examples: In JM KN

PL OP KN

mOK

mLM

mJKO

P, and are diameters, NPM = 46, bisects

and . Find each measure.m KPM,

= 90

= 67

= 316

Type of Bicycle %Comfort 21

Mountain 37Youth 26Hybrid 9Other 7

Example: The table below shows the percent of each type of bicycle sold in the United States in 2001.

Describe the kind of arc associated with each category.

Find the measure of the central angle representing each category.

75.6º133.2º93.6º32.4º25.2º