10-1 circles and circumference
DESCRIPTION
10-1 Circles and Circumference. Circle. The locus of all points in a plane equidistant from a given point called the center . Circles are named by their center point Chord - any segment with endpoints on the circle Diameter - The chord passing through the center of the circle - PowerPoint PPT PresentationTRANSCRIPT
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