Post on 05-Jan-2016
description
Unit Question: What are the properties and
characteristics of circles?
Today’s Question:
How does the measure of an arc compare to the measure of its central angle?
11.1 Parts of a CircleCircle – set of all points _________ from a given point called the _____ of the circle.
C
Symbol:
equidistant
center
C
11.1 Parts of a Circle
P
RADIUS= distance from the _____ to a point on the circle
center
CHORD: a segment whose ________ are on the circle
endpoints
Diameter
P
DIAMETER: distance ______ the circle through its ______
center across
Also known as the longest chord.
What is the relationship between the diameter and the radius of a circle?
r =
OR
D =
½ D
2 r
D = ?
r = ?
r = ? D = ?
Use P to determine whether each statement is true or false.
P
Q
R
TS
diameter. a is .1 RT False
radius. a is .2 PS True
chord. a is .3 QT True
Same center but different radii
P
Q
R
TS
Ex. 4QT. find 7, QP If diameter. a is QT
14
P
Q
R
TS
Ex. 5
Find the measure of radius
PR if PR 3 and QT 5x 6.x
18
P
A
BC
Central Angle : An Angle whose vertex is at the center of the
circleMinor ArcMajor Arc
Less than 180°More than
180°ABACB
To name: use 2 letters
To name: use 3 letters
<APB is a Central Angle
P
E
F
D
Semicircle: An Arc that equals 180°
EDFTo name:
use 3 letters
Measure of an arc is equal to the measure of
the central angle
THINGS TO KNOW AND REMEMBER ALWAYS
A circle has 360 degrees
A semicircle has 180 degrees
Vertical Angles are Equal
Find the measure of an the following arcs.
EB is a diameter.
A
B
C
Q 96m AB
m ACB
m AE
E
=
=
=
96264
84
Tell me the measure of the following arcs.
80100
40
140A
B
C
D
R
m DAB =
m BCA =
240
260