9. Circles...........................................................................................................................................
AboutCircles
LearningObjectives
- Distinguishbetweenradius,diameter, chord,tangent,and secantof a circle.
- Find relationshipsbetweencongruentand similarcircles.
- Examineinscribedand circumscribedpolygons.
- Write the equationof a circle.
Circle,Center, Radius
Acircleis definedas the set of all pointsthat are the samedistanceawayfrom a specificpointcalledthe
centerof the circle.Notethat the circleconsistsof only the curvebut not of the area insidethe curve.The
distancefrom the centerto the circleis calledtheradiusof the circle.
We oftenlabelthe centerwith a capitalletterand we refer to the circleby that letter. For example,the circle
belowis calledcircle or.
CongruentCircles
Two circlesarecongruentif they havethe sameradius,regardlessof wheretheir centersare located.For
example,all circlesof radiusof centimetersare congruentto eachother. Similarly, all circleswith a radius
of milesare congruentto eachother. If circlesare not congruent,then they aresimilarwith the similarity
ratio givenby the ratio of their radii.
Example 1
Determinewhichcirclesare congruentand whichcirclesare similar. For similarcirclesfind the similarity
ratio.