1. 1. 2. 3. 4.

2. C IRCLES Sec: Basic Circles and 12.5 G.11 a,b Circles

3. 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.

4. D EFINITIONS Radius: 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.

5. F ORMULAS All radii are congruent All diameters are congruent d = 2r and r = d/2 or ½ d Ex: a. If DF = 10, find DA b. If PA = 7, find PG c. If AG = 12, find LA A FG L D P

6. C IRCUMFERENCE 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 = 2  r 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. 7cm12.5 in

7. Y OU CAN ALSO USE GEOMETRIC FIGURES TO HELP YOU FIND THE CIRCUMFERENCE OF A CIRCLE Find the exact circumference of P. Ex: P 5 12 the diameter, x = _______ the exact circumference = _______ the approximate circumference = _______ (to the nearest tenth)

8. Standard Equation of a Circle w/center at the origin. x 2 + y 2 = r 2 r is the radius Translation of circles: (x – h) 2 + (y – k) 2 = r 2 (h, k) = Center of the circle r = radius x - shifty - shift GOLDEN RULE

9. T HE CENTER OF A CIRCLE IS THE MIDPOINT OF THE DIAMETER Ex: 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 diameter  Use Midpoint Formula Radius is the distance from the center to any point on the circle.  Use Distance Formula to find the radius. B(5, 4) A(-3, 2)

10. Write the standard equation of the circle: 1. Center (0,1):r = 4 2. Center (1, -1):r = What is the center and radius of each circle: 1. (x - 8) 2 + (y – 4) 2 = 9 2. (x + 2) 2 + (y – 4) 2 = 9

11. ( X – H ) 2 + ( Y – K ) 2 = R 2

15. 1. Write the equation for the given picture: A. Find center: B. Identify radius: C. Plug in equation:

16. S UGGESTED A SSIGNMENTS Classwork: WB pg 327 2-28 even Homework: pg 801-802 8-42 even