By definition,
a circle is the set of all points in a plane that are the same distance from
a fixed point (called its center).
Notes:
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![]() a circle (in green) with center $\,C\,$ |
Depending on context, radius can mean:
The plural of ‘radius’ is either:
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Depending on context, diameter can mean:
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The circumference of a circle is the distance
around the circle.
As discussed below: $$ \cssId{s49}{\text{circumference} = 2\pi r = \pi d\ ,} $$ where $\,r\,$ is the radius and $\,d = 2r\,$ is the diameter. |
![]() circumference of a circle: the distance around the circle |
Compute with circles, and you're certain to run into the special number $\,\pi\ $:
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![]() By definition, $\,\pi\,$ is the ratio of circumference to diameter in a circle: $$ \cssId{s87}{\pi := \frac{\color{blue}{\text{circumference}}}{\color{red}{\text{diameter}}} \approx 3.14} $$ ![]() Thus, $\text{circumference} \approx (3.14)(\text{diameter})$ It takes just over $\,3\,$ diameters to go around the circle! $\pi\,$ is irrational, hence has an infinite, non-repeating decimal expansion $\pi\,$ is approximately 3.1415926535897932384626433832795028841971693993751058209 749445923078164062862089986280348253421170679821480865132 823066470938446095505822317253594081284811174502841027019 385211055596446229489549303819644288109756659334461284756 482337867831652712019091456485669234603486104543266482133 936072602491412737245870066063155881748815209209628292540 917153643678925903600113305305488204665213841469519415116 094330572703657595919530921861173819326117931051185480744 623799627495673518857527248912279381830119491298336733624 |
CENTRAL ANGLE OF A CIRCLEBy definition, a central angle in a circle is an angle formed at the center of a circle by two radii.Notes on central angles:
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On this exercise, you will not key in your answer. However, you can check to see if your answer is correct. |
PROBLEM TYPES:
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