CK12 - Geometry

Example 10

Determineif the circlesgivenby the equations

and

are concentric.

To find the answerto this question,we mustrewritethe equationsof the circlesin standardform and find
the centerpointof eachcircle.

To rewritein standardform,we completethe squareon the and termsseparately.

Firstcircle:

The centerof the first circleis also at point so the circlesare concentric.

Secondcircle:

The centerof the secondcircleis at point.

LessonSummary

In this sectionwe discussedmanytermsassociatedwith circlesand lookedat inscribedand circumscribed
polygons.We also coveredgraphingcircleson the coordinategrid and findingthe equationof a circle.We
foundthat sometimeswe needto use the techniqueof completingthe squareto find the equationof a circle.

LessonExercises

1. Identifyeachof the followingas a diameter, a chord,a radius,a tangent,or a secantline.