This document provides an overview of key concepts about circles including definitions of circles, radii, area, circumference, relationships between radii and chords, and properties of points inside, outside, and on a circle. It concludes with homework assignments practicing these circle concepts.

1. Intro to CirclesAdvanced GeometryFebruary 24, 2010

2. Things we already know…CirclesThe set of all points in a plane that are a given distance (radius) from a given point (center)in the planeRadiusSegment that joins the center to a point on the circleAll radii of a circle are congruentArea of a circleCircumference of a circle

3. Are the circles the same? All circles have the same shape. Their sizes are determined by the radius. If two circles have congruent radii, then the two circles are congruent. If two circles have the same center, then the circles are concentric circles.

4. Where is the point? A point is in the interior of a circle if its distance from the center is less than the radius. d < rA point is in the exterior of a circle if its distance from the center is greater than the radius. d > rA point is on a circle if its distance from the center is equal to the radius. d = r

5. ChordsA chord of a circle is a segment joining any two points on a circle. What is the longest chord of a circle? A diameterof a circle is a chord that passes through the center of the circle.

6. Radius – Chord RelationshipsThe distance from the center of a circle to a chord is the measure of the perpendicular segment from the center to the chord. If a radius is perpendicular to a chord, then it bisects the chord.

7. More RelationshipsIf a radius of a circle bisects a chord that is not a diameter, then it is perpendicular to that chord. The perpendicular bisector of a chord passes through the center of the circle.

8. PracticePage 443 # 5, 6, 12

9. HOMEWORKPage 443 # 8, 14, 23, 24

10. Exit SlipFind the distance from the center of a circle to a chord 30 m long if the diameter of the circle is 34 m.