Pre Algebra (Period 2 & 4)

Circles 9-6

A set of points equidistant from a center point

Radius - one endpoint on circle and one is the center (1/2 diameter)

Diameter - both endpoints on the circle and goes through the center point (twice radius)

Chord - both endpoints on the circle but not necessarily through the center

A VERY SPECIAL RELATIONSHIP WAS FOUND IN B.C.E. TIMES:
IF YOU DIVIDED THE CIRCUMFERENCE BY THE DIAMETER OF ANY SIZE CIRCLE, YOU WOULD ALWAYS GET ABOUT 3.14


Circumference = the circle fence - distance around the circle -
 
(pi)(diameter) = 2(pi)r

If you have radius, double it to get the diameter


Note: the circumference is always about triple the diameter (plus a little bit!)


Circles have 360 degrees and every circle is similar to every other circle


Central angles: vertex is the center point of a circle

Circles have 360 degrees.

So 1/4 of a circle is 90 degrees and 1/2 is 180 degrees


Review central angles with fractions, percents and degrees
We used the example from the book
Lunch (l) 25%
Recreation (r) 20%
Clothes (c) 15%
Savings (s) 40%
We need to change these percents to degrees. WE know that a circle is 360˚
so set up a proportion
% = unknown
100 360

25 = l
100 360
l = 90
so Lunch portion of the circle graph is 90˚

20 = r
100 360

Solve for r
r = 72
so the Recreation portion of the circle graph is 72˚

15 = c
100 360

Solve for c
c= 54
So the clothes portion is 54˚

40 = s
100 360

solve for s
s = 144
so the Savings portion of the cirlce graph is 144˚

Area: Circles 10-3

A = pi ∙ r²