10-1 Circles and Circumference

CircleThe locus of all points in a plane

equidistant from a given point called the center.

Circles are named by their center pointChord- any segment with endpoints on the

circleDiameter- The chord passing through the

center of the circleRadius- a segment whose endpoints are

the center of the circle and a point on the circle

Example:

Circle R has diameters ST and QM If ST=18, find RS If RM=24, find QM If RN=2, find RP

S

Q

R

P

T

MN

Examples:

Diameter of x = 22, diameter of Y =16 and diameter of Z =10

Find EZ and XF

E X YF

Z G

Circumference

The distance around the circleC = πd or C = 2πr

(where π≈3.14, d is diameter and r is radius)

Example: Find circumference if r = 13 inches

Example:

Find the EXACT circumference

23

10-8 Equations of Circles

Standard equation

For a circle with center (h, k) and radius r

x and y are variables and must ALWAYS be in your answer!

222 )()( rkyhx

Example: Write the equation of the circle

With center (-1, 3) and radius

With endpoints of the diameter (4, 6) and (-2, 6)

7

To graph a circle:

Find the center (h, k) (remember that the formula is x-h and y-k

so when naming the center you do the oppositeopposite of the equation)

Find the radius by taking the square root of the number after the =

Plot the center and count out for the radius

Graph each circle:

1622 yx

11)1()2( 22 yx