CK-12 Geometry Concepts

http://www.ck12.org Chapter 9. Circles

Radius of

⊙

A= 3 units

Radius of

⊙

B= 4 units

Radius of

⊙

C= 3 units

From these measurements, we see that
⊙
A∼=
⊙
C.

Notice thecircles are congruent. Thelengths of the radiiareequal.

Watch this for help with the Examples above.

MEDIA

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CK-12 Foundation: Chapter9PartsofCirclesB

Concept Problem Revisited

Refer to the photograph in the “Concept” section at the beginning of this Concept. The orange line (which is normally
black, but outlined for the purpose of this exercise) is a diameter of the smaller circle. Since this line passes through
the center of the larger circle (yellow point, also outlined), it is part of one of its diameters. The “moon” hand is a
diameter of the larger circle, but a secant of the smaller circle. The circles are not concentric because they do not
have the same center and are not tangent because the sides of the circles do not touch.

Vocabulary

Acircleis the set of all points that are the same distance away from a specific point, called thecenter. Aradiusis
the distance from the center to the outer rim of a circle. Achordis a line segment whose endpoints are on a circle.
Adiameteris a chord that passes through the center of the circle. The length of a diameter is two times the length
of a radius. Asecantis a line that intersects a circle in two points. Atangentis a line that intersects a circle in
exactly one point. Thepoint of tangencyis the point where the tangent line touches the circle.Tangent circlesare
two or more circles that intersect at one point.Concentric circlesare two or more circles that have the same center,
but different radii.Congruent circlesare two or more circles with the same radius, but different centers.

Guided Practice

1. If the diameter of a circle is 10 inches, how long is the radius?


2. Is it possible to have a line that intersects a circle three times? If so, draw one. If not, explain.


3. Are all circles similar?

Answers:

1. The radius is always half the length of the diameter, so it is 5 inches.


2. It is not possible. By definition, all lines are straight


3. Yes. All circles are the same shape, but not necessarily the same size, so they are similar.