10 1 circles and circumference
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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

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10-1 Circles and Circumference

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10 1 circles and circumference

10-1 Circles and Circumference


Circle

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

  • Radius- a segment whose endpoints are the center of the circle and a point on the circle


Example

Example:

  • Circle R has diameters ST and QM

    • If ST=18, find RS

    • If RM=24, find QM

    • If RN=2, find RP

Q

P

S

R

T

N

M


Examples

Examples:

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

  • Find EZ and XF

X

Y

Z

E

G

F


Circumference

Circumference

  • The distance around the circle

  • C = πd or C = 2πr

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

    Example: Find circumference if r = 13 inches


Example1

Example:

  • Find the EXACT circumference


10 8 equations of circles

10-8 Equations of Circles


Standard equation

Standard equation

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

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


Example write the equation of the circle

Example: Write the equation of the circle

  • With center (-1, 3) and radius

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


To graph a circle

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 opposite 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

Graph each circle:


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