Brain TrainerBrain Trainer

Find the following measures.Find the following measures.

1) Arc RJ1) Arc RJ

2) m<JSL2) m<JSL

3) Arc JL3) Arc JL

4) 4) Name a major arc.Name a major arc.

5) 5) Name a minor arc.Name a minor arc.

6) 6) Name a semicircle.Name a semicircle.

SR

J

L1700

E

Arcs and ChordsArcs and Chords

Lesson 10.3Lesson 10.3

Indiana Standard G.6.2Indiana Standard G.6.2

Arcs and ChordsArcs and Chords

The endpoints of a chord are also endpoints The endpoints of a chord are also endpoints of an arc. of an arc.

Arc AB starts at point A and ends at point B.Arc AB starts at point A and ends at point B.

A B

Arcs and ChordsArcs and Chords

In a circle or in congruent circles, 2 minor In a circle or in congruent circles, 2 minor arcs are congruent if and only if their arcs are congruent if and only if their corresponding chords are congruent.corresponding chords are congruent.

If chords AB and CD If chords AB and CD are are congruent, then congruent, then arcs AB arcs AB and CD are and CD are congruent.congruent.

A

B

C

D

ExampleExample

Assume AB and XY are congruent.Assume AB and XY are congruent.

AB AB

XYXYA

B

X

Y10

25

10

25

Inscribed PolygonsInscribed Polygons

The chords of adjacent arcs can form a The chords of adjacent arcs can form a polygon. A polygon is inscribed if all of its polygon. A polygon is inscribed if all of its vertices lie on the circle.vertices lie on the circle.

Circle A is CIRCUMSCRIBED about the polygon because it contains all the vertices of the polygon.

. AQ

R

S

T

U

Diameters and ChordsDiameters and Chords

In a circle, if a diameter (or radius) is In a circle, if a diameter (or radius) is perpendicular to a chord, then it bisects the perpendicular to a chord, then it bisects the chord and its arc.chord and its arc.

If BA TV, thenIf BA TV, then

UT = UV and AT = AVUT = UV and AT = AV. C

U

B

A

VT

~ ~

ExamplesExamples

CD = 24, radius = 13CD = 24, radius = 13

mCD = 134, find mCBmCD = 134, find mCBFind DSFind DSFind PSFind PS(Hint: use pythagorean theorem)(Hint: use pythagorean theorem)

121222 + (x) + (x)22 = 13 = 132 2

(x)(x)2 2 = 25 = 25 PX = 5PX = 5

. 13

C

D

B

P

S67

1212

x

Homework Homework

Marker Board!Marker Board!

Last exampleLast example

AB = 20, radius = 15AB = 20, radius = 15

Find EFFind EF

FB = 10FB = 10

10102 2 + x + x22 = 15 = 1522

xx22 = 125 = 125 EF = 11.18EF = 11.18 A B

C

D

. E

F

15

10

x

Problem 1Problem 1

Solve for x.Solve for x.

A

B

C

D2x - 12

3624

Problem 2Problem 2

A

B

C

D14

14

(x + 17)0

Solve for x.

(4x + 2)0

5

Problem 3Problem 3

AB = 12, radius = 8AB = 12, radius = 8

mAB = 72, find mCBmAB = 72, find mCB

Find AFFind AF

Find EFFind EF(Hint: use pythagorean theorem)(Hint: use pythagorean theorem)

A B

C

D

. E

F

8

6

5.3x

Problem 4Problem 4

AB = 26, radius = 20AB = 26, radius = 20

mAB = 24, find mACmAB = 24, find mAC

Find BFFind BF

Find EFFind EF(Hint: use pythagorean theorem)(Hint: use pythagorean theorem)

A B

C

D

. E

F 13

2015.2

x

Problem 5Problem 5

CD = 32, radius = 22CD = 32, radius = 22

mCD = 100, find mCBmCD = 100, find mCB

Find DLFind DL

Find PLFind PL(Hint: use pythagorean theorem)(Hint: use pythagorean theorem)

16

.

C

D

B

P

L

22

15.1

x

Problem 6Problem 6

CD = 42, radius = 25CD = 42, radius = 25

mCD = 24, find mBDmCD = 24, find mBD

Find CAFind CA

Find PAFind PA(Hint: use pythagorean theorem)(Hint: use pythagorean theorem)

21

.

C

D

B

P

A

25

13.6

x