Skills #2Skills #21. What symbol is used to name circle M?1. What symbol is used to name circle M?2. The distance from the center to a point on a circle 2. The distance from the center to a point on a circle is __________.is __________.3. The distance across a circle through the center is a 3. The distance across a circle through the center is a ___________.___________.4. A chord is a segment whose _________ are on the 4. A chord is a segment whose _________ are on the circle.circle.5. A secant is a line that intersects at circle in _______ 5. A secant is a line that intersects at circle in _______ points.points.6. A tangent is a line that intersects a circle at 6. A tangent is a line that intersects a circle at exactly ________ points.exactly ________ points.7. The point where a tangent intersects a circle is a 7. The point where a tangent intersects a circle is a _____________._____________.8. A tangent is ___________ to a radius of the circle.8. A tangent is ___________ to a radius of the circle.9. If 2 tangent lines originate at the same external 9. If 2 tangent lines originate at the same external point, the tangents are ______________.point, the tangents are ______________.10. A common internal tangent intersects the 10. A common internal tangent intersects the segment between the ________________ of a circle.segment between the ________________ of a circle.

Table of Contents Table of Contents 39. Section 10.2 Arcs and 39. Section 10.2 Arcs and

ChordsChords

10.2 Arcs and chords10.2 Arcs and chords

Essential Question – How are Essential Question – How are the angles made by arcs and the angles made by arcs and

chords related?chords related?

Central angleCentral angle

• Central angle-Central angle- angle whose vertex is angle whose vertex is the center of a circle the center of a circle

A

B

C ACB is ACB is a central a central angleangle

ArcsArcs

• Arc-Arc- a piece of the outline of a circle. a piece of the outline of a circle.

Named with 2 or 3 letters Named with 2 or 3 letters

Measured in degreesMeasured in degrees

B

P

BP

(

Major and minor arcsMajor and minor arcs

• Minor arc-Minor arc- part of the outline of a part of the outline of a circle that measures less than 180circle that measures less than 180oo (named by 2 letters).(named by 2 letters).

• Major arc-Major arc- part of the outline of a part of the outline of a circle that measures between 180circle that measures between 180oo and 360and 360oo. .

(needs three letters to name)(needs three letters to name)ABC

(

(

http://www.mathopenref.com/arcminormajor.html

AC

Arc measuresArc measures

• Measure of a minor arc-Measure of a minor arc- measure of measure of its central angleits central angle

• Measure of a major arc-Measure of a major arc- 360 360oo minus minus measure of minor arcmeasure of minor arc

Ex: find the arc measuresEx: find the arc measures

A

B

C

D

E

50o

m AB=

m BC=

m AEC=

m BCA=

50o

130o

180o

180o+130o = 310o130o

180o(

((

(

OR 360o- 50o = 310o

Arc additionArc addition

• The measure of an arc formed by two The measure of an arc formed by two adjacent arcs is the sum of the adjacent arcs is the sum of the measures of those arcs.measures of those arcs.

AB

Cm ABC = m AB+ m BC

( ( (

Congruent arcsCongruent arcs

• Congruent arcs-Congruent arcs- 2 arcs with the same 2 arcs with the same measuremeasure

• MUST be from the same circle OR MUST be from the same circle OR circles!!!circles!!!

ExampleExample

30o

30o

A

B

C

DE

m AB=30o

m DC=30o

AB DC

((

( (

ExampleExampleA

B

C

DE

45o

m BD= 45o

m AE= 45o

BD AE

((

( (

The arcs are the same measure; so, why aren’t they ?

The 2 circles are NOT !

Congruent minor arcsCongruent minor arcs• In the same circle (or in In the same circle (or in circles), 2 circles), 2

minor arcs are minor arcs are iff their iff their corresponding chords are corresponding chords are ..A

B

C

AB BC iff AB BC

( (

Ex: find m BCEx: find m BC

A

B

CD

3x+11 2x+47

BD BC.

3x+11=2x+47x=36

2(36)+4772+47119o

(

( (

Diameters and chordsDiameters and chords• If a diameter of a circle is If a diameter of a circle is to a to a

chord, then the diameter bisects the chord, then the diameter bisects the chord and its arc.chord and its arc.

E

DG

CF

If EG is to DF, then DC CF and DG GF

( (

Congruent chordsCongruent chords• In the same circle (or in In the same circle (or in circles), 2 circles), 2

chords are chords are iff they are equidistant iff they are equidistant from the center.from the center.

D C

A

G F

E B

DE CB iff AG AF

Ex: find CG.Ex: find CG.

A

B

C

E

F

D

6

6

6

6

7

G72=CF2+62

49=CF2+3613=CF2

CF CG

CF =

CG =

13

13

AssignmentAssignment

Pg. 607: 13-37 odd, 45, 47

AssessmentAssessment