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P ARTS OF CIRCLE C F E AB P Name a circle by its center. P CP is radius AB is Diameter EF is a chord Note: AB is also a chord.
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PARTS OF CIRCLE
C
F
E
A BP
Name a circle by its center.
P
CP is radius
AB is Diameter
EF is a chordNote: AB is also a chord.
DEFINITIONSRadius:
is a segment w/one endpoint at the center of the circle and the other endpoint on the circle. All radii of a circle are congruent.
Chords:are segments that have both their endpoints on the circle. (i.e. it goes from one side of the circle to the other.)
Diameter:a chord that goes through the center of a circle.
FORMULAS All radii are congruent All diameters are congruent
d = 2r and r = d/2 or ½ d
Ex:a. If DF = 10, find DAb. If PA = 7, find PGc. If AG = 12, find LA
A
FG
L
D P
CIRCUMFERENCE The circumference of a circle is the distance
around the circle. (To fine circumference you have to walk on the edge)
Formulas:C = d or C = 2r
Note : (pi) has a key on the calculator; accepted value: 3.14
Ex: Find the circumference, diameter and radius.a) Find C if r = 7cm b) Find C if d = 12.5 in
c) Find d and r to the nearest hundredth if c = 136.9 meters.
7cm 12.5 in
YOU CAN ALSO USE GEOMETRIC FIGURES TO HELP YOU FIND THE CIRCUMFERENCE OF A CIRCLE
Find the exact circumference of P.
Ex:
P5
12
x4
3
the diameter, x = _______
the exact circumference = _______
the approximate circumference = _______(to the nearest tenth)
Standard Equation of a Circle w/center at the origin.x2 + y2 = r2
r is the radius
Translation of circles:(x – h)2 + (y – k)2 = r2
(h, k) = Center of the circle
r = radiusx - shift y - shift
GOLDEN RULE
THE CENTER OF A CIRCLE IS THE MIDPOINT OF THE DIAMETEREx: is a diameter of the circle. Find the
coordinates of the center and the length of the radius of the circle.
Center (P) = Midpoint of the diameterUse Midpoint Formula
Radius is the distance from the center to any point on the circle.
Use Distance Formula to find the radius.
AB
B(5, 4)
A(-3, 2)
Write the standard equation of the circle:1. Center (0,1):r = 42. Center (1, -1):r =
What is the center and radius of each circle:3. (x - 8)2 + (y – 4)2 = 94. (x + 2)2 + (y – 4)2 = 9
4
(X – H)2 + (Y – K)2 = R2
(X – H)2 + (Y – K)2 = R2
(X – H)2 + (Y – K)2 = R2
(X – H)2 + (Y – K)2 = R2
1. Write the equation for the given picture:
A. Find center:B. Identify radius:C. Plug in equation:
SUGGESTED ASSIGNMENTSClasswork: WB pg 327 2-28 even
Homework: pg 801-802 8-42 even
