CIRCLES

Unit 9; Chapter 10

Tangents to Circles lesson 10.1California State

Standards

7: Prove and Use theorems involving properties of

circles.21: Prove and Solve

relationships among chords, secants

and tangents.

Lesson Goals

Identify lines and segments in circles.Give the equation for a tangent line on the coordinate plane.Recognize tangent and concentric circles.

ESLRs: Becoming Effective Communicators, Competent Learners and Complex Thinkers

definitionsCircle

The set of all points in a plane that are equidistant

from a given point.Center

The given point.Radius

A line segment with the center as one endpoint and

a point on the circle as the other endpoint.The distance from the center to a point on the circle.

definitionsCircle

The set of all points in a plane that are equidistant

from a given point.Center

The given point.Radius

A line segment with the center as one endpoint and

a point on the circle as the other endpoint.The distance from the center to a point on the circle.

C

P

the plural of radius is radii

a circle is namedby its center

C

is a radius is the lengthCPCP

definitionsCongruent Circles

Circles with the same radiusDiameter

A line segment with endpoints on the circle that contains the center of the circle.

The distance across a circle through the center. 2r = d

Congruent CirclesCircles with the same radius

DiameterA line segment with endpoints on the circle that contains the center of the circle.The distance across a circle through the center. 2r = d

definitions is a diameterRP

PCR

C R RX CY

2r = dX

Y

definitionsChord

A segment whose endpoints are on the circle.A diameter is a “specialized” chord.

SecantA line that intersects a circle in two points.A chord is part of a secant.

TangentA line that intersects a circle in exactly one point.The circle and line must lie in the same plane.

ChordA segment whose endpoints are on the circle.A diameter is a “specialized” chord.

SecantA line that intersects a circle in two points.A chord is part of a secant.

TangentA line that intersects a circle in exactly one point.The circle and line must lie in the same plane.

definitions

CA

B is a chordAB

F

G is a secantFG

0

T is a tangentTU

0 U

radiusC

P

A

B

Q

X

radiu

s

radiu

sdia

meter

chord

secant

tangent

Identify each line or segment

chord

QA0

QX0

AB QA CA CP CB BP

point oftangency

definitionTangent Circles

Coplanar circles that intersect in exactly one point.

internally tangent circles

definitionTangent Circles

Coplanar circles that intersect in exactly one point.

externally tangent circles

definitionConcentric Circles

Coplanar circles with a common center.

definitionCommon Tangent

A line or segment that is tangent to two coplanar circles

• Common Internal Tangent crosses between the circles• Common External Tangent stays along the edges of the

circles

Common TangentA line or segment that is tangent to two

coplanar circles• Common Internal Tangent crosses between the circles• Common External Tangent stays along the edges of the

circles

definitionCommon Internal Tangent

Common External Tangent

example

Is the common tangentinternal or external?

external

C D T

example

C

H

B

A I

D

E

F G

Describe each segmentand line

tangentdiameter

chordradiussecant

EIDFCE

Point of tangencyradius

definitions

exteriorinterior

Interior of a CircleThe set of points inside the circle

Exterior of a CircleThe set of points outside the circle.

exampleWhat are the coordinates of each center?

What is the radius of each circle?

x

y

A B

(2, 2)A (6, 2)B

2A r 2B r

A B

exampleDescribe the intersection of the two circles.

x

y

A B

(4,2)

exampleDescribe the common tangents of the circles.

x

y

A B

and have anintenal tangent at 4A B

x

They have 2 external tangents.

4y 0y

A

y

example

B

What are the coordinates of each center? (0,1)A (2,1)B

What is the radius of each circle? 1A r 3B r

Describe any common tangents.x 1 is a

common external tangentx

22

Today’s Assignment

Tribe Pride

always my best effort.

p. 599: 10 – 16 e, 18 – 35

10. The diameter of a circle is 6.7 inches. Find the radius.12. The diameter of a circle is 8 cm. Find the radius.14. The radius of a circle is 62 ft. Find the diameter.16. The radius of a circle is 4.4 cm. Find the diameter.

#29 - 31Copy the diagram. Tell how many common tangentsthe circles have. Then sketch the tangents.

Match the notation with the term that best describes it.

#26 - 28Tell whether the tangent(s) are internal or external