Chapter 9 Circles (page 328) How can relationships in a circle allow you to solve problems involving segments, angles, and arcs?

Circles are all around us! Can you identify the following circles?

Lesson 9-1 Basic Terms (page 329) Essential Question What are the characteristics of a circle or a sphere?

Basic Terms

CIRCLE the set of all points in a plane at a given distance from a given point. O example:  O

CIRCLE the set of all points in a plane at a given distance from a given point. Q example:  Q

RADIUS the given distance in the circle definition. O radius

RADIUS ALSO any segment joining the center of the circle to a point on the circle. O radius Plural is radii.

CHORD a segment whose endpoints lie on a circle. O radius chord

DIAMETER a chord that contains the center of a circle. O radius chord diameter

DIAMETER ALSO has length equal to twice a radius, ie. d = 2 r. O radius = r chord diameter d = 2r

SECANT A line that contains a chord of a circle. Q secant

TANGENT a line in the plane of a circle that intersects the circle in exactly 1 point. Q secant tangent

TANGENT The point of intersection is called the point of tangency. Q secant tangent point of tangency

circle 2-D

sphere 3-D

SPHERE the set of all points in space at a given distance from a given point. X example: sphere X

NOTE Many of the terms used with circles are also used with spheres. X center: X

X radii F AC

X chords F AC E D B

X secants F AC E D B

Tangent n X F AC E D B Point of Tangency B n

CONGRUENT CIRCLES circles that have congruent radii. D example  D &  P P

CONGRUENT SPHERES spheres that have congruent radii. real life examples … Sports balls … soccer, baseball, etc. Candy … Bubble gum balls What are some other examples?

CONCENTRIC CIRCLES circles that lie in the same plane and have the same center.

CONCENTRIC SPHERES spheres that have the same center. real life examples … Sports balls … baseball, golf ball, etc. Candy … Everlasting Gobstoppers Planets … Earth’s layers

INSCRIBED POLYGON a polygon is inscribed in a circle if each vertex of the polygon lies on the circle.

CIRCUMSCRIBED CIRCLE a circle is circumscribed about a polygon if each vertex of the polygon lies on the circle.

INSCRIBED POLYGON and CIRCUMSCRIBED CIRCLE are the same thing!

Take a look at Written Exercises on page 331, #4 key term - Great Circle What are the characteristics of a circle or a sphere?

Assignment Written Exercises on pages 330 & 331 GRADED: 1 to 11 odd numbers What are the characteristics of a circle or a sphere?