CK12 - Geometry

The diagramreviewsthe namesfor the “parts”of a circle.

• The center


• The circle:the pointsthat are a givendistancefrom the center(whichdoesnot includethe centeror in-
  terior)


• The interior:all the points(includingthe center)that are insidethe circle


• circumference:the distancearounda circle(exactlythe sameas perimeter)


• radius:any segmentfromthe centerto a pointon the circle(sometimes“radius”is usedto meanthe
  lengthof the segmentand it is usuallywrittenas )


• diameter:any segmentfroma pointon the circle,throughthe center, to anotherpointon the circle

(sometimes“diameter”is usedto meanthe lengthof the segmentand it is usuallywrittenas )

If you like formulas,you can alreadywriteone for a circle:

or

CircumferenceFormula

The formulafor the circumferenceof a circleis a classic.It has beenknown,in roughform,for thousands
of years.Let’s look at one way to derivethis formula.

Startwith a circlewith a diameterof unit. Inscribea regularpolygonin the circle.We’ll inscriberegular
polygonswith moreand moresidesand see whathappens.For eachinscribedregularpolygon,the
perimeterwill be given(howto figurethat is in a reviewquestion).

Whatdo you notice?

1. The moresidesthereare, the closerthe polygonis to the circleitself.


2. The perimeterof the inscribedpolygonincreasesas the numberof sidesincreases.


3. The moresidesthereare, the closerthe perimeterof the polygonis to the circumferenceof the circle.

Now imaginethat we continuedinscribingpolygonswith moreand moresides.It wouldbecomenearlyim-
possibleto tell the polygonfrom the circle.The tablebelowshowsthe resultsif we did this.

RegularPolygonsInscribedin a Circlewith Diameter