Circles

Day Topic Assignment Completed

Day 1 Circles and Circumference

D1 HW – SP 10-1

Day 2 Measures of Arcs and Angles

D2 HW – Pg. 9

Day 3 Arcs and Chords D3 HW – SG 10-3

Day 4 Arcs and Chords D4 HW – SP 10-3

Day 5 Inscribed Angles D5 HW – Pg. 19

Day 6 Inscribed Angles D6 HW – SP 10-4

Day 7 Tangents and Secants D7 HW – SP 10-5 (1, 2, 5, 6)

Day 8 Tangents and Secants D8 HW – Pg. 26

Day 9 Angle Relationships in Circles

D9 HW – Pg. 29 and SP 10-6 (1 – 6)

Day 10 Angle Relationships in Circles

D10 HW – Pg. 32 and SP 10-6 (7 – 12)

Day 11Segment Relationships in

Circles D11 HW - Pg. 35

Day 12 Segment Relationships in Circles

D12 HW – Pg. 39 and rest of SP 10-7 if not finished in class.

Day 13 Equations of Circles D13 HW – Pg. 43

Day 14 Review Study

Day 15 TEST Good Luck!

1

Circles and Circumference A circle is the set of points in a plane equidistant, called the radius, from a given point called the center of the circle.

Naming a Circle:Name the circle according to the center point.

The name of the circle is circle P or • P. P

Segments that intersect a circle have special names.

Segments that Intersect Circles A radius (plural radii) is a

segment with endpoints at the center and on the circle.

A chord is a segment with endpoints on the circle. Chords do not go through the center of the circle.

A diameter is a segment that passes through the center of the circle and has endpoints on the circle. (Collinear radii.)

Use the diagram to answer the questions.

1. _____ is the name of the circle.

2. _____ is the diameter.

3. _____ is a chord.

4. _____, _____, and _____ are the radii.

5. All the radii are _____ to each other.

2

FE

D

C

B

A

AB is a chord.EC is a diameter.

EF, FC, and FD are all radii. All the radii are .

PL

M

N

Radius and Diameter RelationshipsRadius Formula:

r = or r = d

***All radii in a circle are .

Diameter Formula:d = 2r

1. If the radius of a circle is 10, what is the diameter?

2. If the diameter of a circle is 14, what is the radius?

Use the diagram to answer the following questions.

3. If TV = 8, what is the UQ?

4. If QU = 12, what is QT?

5. If QU = 30, what is:

a. QT?

b. TV?

c. TU?

Circle Pairs

Congruent Circles – two circles are congruent if they have congruent radii.

GH JK, so • G • J

Concentric Circles – coplanar circles that have the same center.

• A with radius AB and • A with radius AC are concentric.

Two circles can intersect in two different ways:2 Points of Intersection 1 Point of Intersection No Points of Intersection

1. If RT = 21, what is the length of QV?

3

U

Q

V

T

H

GJ

K

B

C

A

•

2. The radius of • S is 15 units, the radius of • R is 10 units, and DS = 9 units. Find:

a. CD = _____

b. RC = _____

3. The diameter of • Y is 22 units, the diameter of • X is 16 units, and

WZ = 5 units. Find XY.

Circumference

1. Find the circumference of a circle whose diameter is 10 cm. to the nearest tenth of a cm.

2. Find the exact circumference of a circle whose diameter is 4 in.

4

R S

V

Q T

R

SC D

X ZW Y

Circumference – Distance around a circle.,C = d

Chocolate pie’s() delicious.

3. Find the exact circumference of a circle whose radius is 7 units.

4. Find the diameter of a circle to the nearest hundredth if the circumference is 106.4 in.

5. Find the diameter of a circle to the nearest tenth if the circumference is 65.4 ft.

A polygon is inscribed in a circle if all the vertices lie on the circle.A circle is circumscribed about a polygon if it contains all the vertices of the polygon.

6. A square with side length of 9 in. is inscribed in • J. Find the exact circumference.

7. A square with side length of 10 ft. is inscribed in • J. Find the exact circumference.

Measuring Angles and Arcs

5

•J

•J

Arcs and Arc Measures Minor Arc

A minor arc is the shortest arc connecting two endpoints on a circle.

It’s measure is less than 180. It is equal to the central angle.

Major Arc A major arc is the longest arc

connecting two endpoints on a circle.

major arc = 360 – x.

Semicircle (half circle) A semicircle is an arc with

endpoints that lie on a diameter. It is equal to 180. m = 180

m = 180

Each half circle = 180.

Identify each arc as a major arc, minor arc or semicircle of the circle.

1. m 2. m 3. m

6

A

•

100

30

C

E50

R

D

B

FE

D

C

CED is a major arc. m = 360 – 93 = 267

CD is a minor arc. m = 93

93

D

A BC

E

Central AnglesCentral Angle

A central angle is an angle with its vertex in the center of the circle.

It is equal to the arc it intercepts.

If m = 93, then mDFC = 93.

Sum of Central Angles The sum of the all measures of

the central angles in a circle is equal to 360.

m1 + m2 + m3 = 360 •

4. m 5. m 6. m

7. PR and QT are diameters. Find the measure of each arc.

a. m b. m c. m

d. m e. m f. m

7

U

R

QP

T

40

S

A40 50

F

C

DDFC is a central angle. mDFC = 9393

B2

A 13

g. m h. m

Find the value of x.

1. 2. 3.

4. 5. 6.

7. Find the value of x.

8. In the accompanying diagram of circle O, has a measure of

200°. What is the mBOA?

8

x130 145

175 xx40 85

x

140

x

112 33

x

T

U

R

V

8x - 4

13x - 3

5x + 520x

Q S

9. If m BOC = 15, find:

a. mAOC

b. m

c. m

d. m

e. m

10. In circle O, AB is a diameter and mAOC = 100. Find:

a. mCOB

b. m

c. m

d m

9

O

C

A

B

100

OC

A B

e. m

f. m

11.Find the value of x.

D2 HW - Arcs and Central Angles

1. In circle O, m AOB = 87, m BOC = 93, and m COD = 35. Find the measure of each of the following:

a. DOA b. c.

d. e. f.

g. h. i.

10

O

C

A

B

D

2. Lines AB and CD intersect at O, the center of the circle, and mAOC = 25. Find the measure of each of the following:

a. COB b. BOD c. DOA

d. e.

f.

g. h. i.

3. In circle O, AOC and COB are supplementary. If m AOC = 2x, m COB = x + 90, and m AOD = 3x + 10, find:

a. x b. m AOC c. m COB

d. m AOD e. m DOB f. m

g. m h. m

i. m

11

O

B

A

C D

j. m k. m

l. m

Arcs and Chords

Congruent arcs have the same measure.Congruent Arcs, Chords, and Central Angles

If mBEA mCED, then BA CD.

If BA CD, then

.If ,

then mBEA mCED.Congruent central

angles have congruent chords.

Congruent chords have congruent arcs.

Congruent arcs have congruent central

angles.

1. The mBEA = 82 and the measure of chord CD = 10.

a. What is the mCED?

b. What is the measure of chord BA?

c. What is the mBEC?

12

B

A D

C

E

B

A D

C

E

B

A D

C

E

B

A D

C

E

2. The measure of chord CD = 8 and m = 76.

a. What is the measure of chord BA?

b. What is the m ?

3. The m = 86.

a. What is the m ?

b. What is the mCED?

c. What is the mBEA?

4. QR ST. Find m ?

13

B

A D

C

E

B

A D

C

E

R

Q

T

S

4x

3x + 22

5. The mHLG mKLJ. Find m .

6. Find the value of x.

a. b.

.

c. d. • J • K

Bisecting Arcs and Chords

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

Note:

14

H

G K

J

2x + 5 x + 13

L

D

E G

F

x 120

R

Q

T

S

8x2x + 3 •O

P

Q3x - 7 •K

M

N

2x + 1 •J

H

G K

J

x 80

L

D

B

AC

E

You can use the Pythagorean Theorem to find the lengths. By drawing in a radius, you create a right triangle.BE, ED, and EA are radii.

Since EA BD, then AE bisects BD

Therefore, BC CD and

.

1. In • S, m = 98. Find m .

2. In • S, TR = 6. Find PR.

3. In • S, if diameter QST chord PR at V. If PR = 18, find PV and VR.

4. In • J, GH KM. If JL = 8 and KM = 30, find the length of KJ.

15

Q

R

STP

6

Q

R

STP

V

Q

RS

T

P

L

G

MJ

H

K

5. In • J, GH = 34 and KM = 30. Find the length of JL.

6. Find TV to the nearest tenth.

16

L

G

MJ

H

K

5

T

R

V

6U S

Chords Equidistant from Center

In the same circle or in congruent circles, two chords are congruent if and only if they are equidistant from the center.

If FG JH, then LX = LY.

1. In • A, WX = XY = 22, BE = 5x, and CE = 3x + 4. Find EB.

2. In • H, PQ = 3x – 4 and RS = 14. Find x.

17

L

XH

G

J

FY

T8

UH

R

P S

Q

8

W

B C

YE

3x + 45x

X

Inscribed Angle TheoremInscribed Angle

An inscribed angle is an angle with its vertex on the circle.

It is equal to ½ the arc it intercepts.

Note: The arc is equal to 2 times the angle.

If m = 100, then mDFC = 50.

Inscribed AnglesIf inscribed angles of a circle intercept the same arc, then the angles are congruent.

ABC and ADC intercept , so

that ABC = ADC.

An inscribed angle intercepts a diameter or semicircle if and only of the angle is a right angle.

If is a semicircle (180), then mC = 90.

If mC = 90, then = 180 (semicircle) and

AB is a diameter.

1. Find mN. 2. Find mN. 3. Find mN.

18N

M

L

80

N

K

L

62

F

C

DDFC is an inscribed angle. mDFC = ½ (100) = 50100

E

C

BD

AC

B

A

D

N

K

L

35

4. Find m 5. Find m . 6. Find m

.

7. Find mLMP and m . 8. Find mGFJ and m .

9. Find mP and m . 10. Find mC and m

.

19

B

C

A72

B

C

A100

P

S

Q113

R

P

M

L 48N

36 J

H

F 110

G

36

N

P

M70

O56

D

F

C

98

E

40

11. Find mACB and mAOB. 12. Find mC and m .

13. Find:

a. m b. m c. m

d. mABE e. mAOC f. mBAC

14. Find x. 15. Find mFJH.

20

50AO

C

124

B

E

P

SQ5x + 8

RG

J

F5x

H4x + 9

A

OC

86

B

A

88

C

80

B

16. Find mT . 17. Find mF.

18. In the diagram of circle O, diameters AOB and COD are drawn as well

as chords AC, CB, and DB. If mACD = 32 and = 116, find:

a. m b. m c. m

d. mAOC e. mAB f. mCBD

g. mBOD h. mACB

21

U

T

S

3x - 5

V2x + 15

J

G

H

4x + 2F

9x - 3

116

32

O

D

C

BA

Inscribed Angle TheoremIf a quadrilateral is inscribed in a circle, then its opposite angles are supplementary.

A and C are supplementary. mA + mC = _____.

B and D are supplementary. mB + mD = _____.

ABCD is inscribed in • E.

1. Find the value of x. 2. Find mB.

3. Find all the angle measures of each quadrilateral.

a. b.

x = _____ x = _____

mR = _____ mJ = _____

mS = _____ mK = _____

mT = _____ mL = _____

mV = _____ mM = _____D5 HW - Inscribed Angle

22

CA E

D

B

G

F

H

3x + 5E 4x C

B

D

2x - 30

A

x

T

S

V

8x + 8

R 7x 11x L

K

M

x + 25

Jx - 17

2x + 2

1. Find each measure.

a. mN. b. mN. c. mN.

d. m e. m . f. m .

g. Find x. h. mH and mG i. mT and mV

23

B

C

A102

P

S

Q118

R

N

M

L

92

N

K

L

51

N

K

L 210

124

B

C

A 48

P

SQ

x R

2x

G

J

F 32

H5x + 4

6x - 2

T

S

V 2x + 30

R 45

4x

Tangents and Secants

Lines That Intersect Circles

A secant is a line or ray that intersects a circle at two points.

A tangent is a line or ray that intersects the circle at exactly one point, called the point of tangency.

Tangent Circles

Two coplanar circles that intersect at exactly one point are called tangent circles.

1. Identify each line or segment that intersects each circle.

a. b.

Line l is a ____________. Line NM is a ____________.

Line m is a ____________. Ray LM is a ____________.

24

points of tangency

A

C

B

l

C is the point of tangency.

l is a tangent.

AB is a secant.

m

G

F

H

l NK

MJ

L

FG is a ____________. KJ is a ____________.

2. Use circle P to identify each line, segment or point.

a. secant line _____

b. point of tangency _____

c. tangent line _____

d. chord _____

e. a point in the exterior of the circle _____

f. a point in the interior of the circle _____

3. In each figure, draw the common tangents. If no common point exists, state no common tangent.

a. b. c.

The shortest distance from a tangency to the center of a circle is the radius drawn to the point of tangency.

Angle Formed by a Tangent and a Radius Theorem

A line is a tangent to a circle if it is perpendicular () to a radius drawn to the point of tangency.

25

Y

k

P

z

X

B

R

CA

E

B

1. EA is a __________.

2. Line BAC is a _______________ line.

3. A is the point of _______________.

4. EAC and EAB are __________ angles.

5. mEAC = _____ and mEAB = _____.

6. Tangent BA intersects radius OA. What is mOAB?

7. JK is a radius of • J. Determine whether KL is a tangent to • J. Justify your answer.

a. b.

8. JH is tangent to • G. Find the value of x.

a. b.

9. BC is tangent to • A. Find the value of x to the nearest tenth.

26

CA

E

B

B

O A

L

J

K 9

8

15 L

J

K 12

6

8

G

J

8x

12 H

G

J

4x

2H

A

C14 x

17B

More than one line can be tangent to a circle.Congruent Tangents

If two segments are tangent to a circle from the same external point, then the segments are congruent.

EF and EG are tangent to • C.

FE GE

1. AC and BC are tangent to • D. Find the value of x.

2. QR and SR are tangent to • T. Find the value of x.

3. WX and YX are tangent to • Z. Find the value of WX and YX.

27

E

F

G

C

external point

2x - 5

A

D

B

x + 15C

26

Q

T

S

3x + 8

R

3x + 6

W

Z

Y

2x + 9

X

Circumscribed Polygons Circumscribed NOT Polygons

A polygon is circumscribed about a circle if every side of the polygon is tangent to the circle.

1. Triangle ABC circumscribes circle G. Find:

a. AE

b. DC

c. CF

d. perimeter of ABC

2. Quadrilateral RSTU is circumscribed about circle J. If the perimeter is 18 units, find x.

.

3. Triangle JKL is circumscribe about circle R. Find:

a. x.

b. the perimeter of JKL.

c. What type of triangle is JKL?

28

G

A

BC

7

8E

F

D

10

B U

C

RD

Tx

A

S

x

33

R

K

LJ

x + 3

7N

O

M

4x - 97

Vocabularypoint of tangency exterior tangent line secantchord interior perpendicular tangent

29

A _____________ is a line that intersects a circle at two points.Ex: Line _____

A _____________ is a segment whose endpoints lie on the circle.Ex: Segment _____

A _____________ is a line that intersects the circle at exactly one point.Ex: Line _____

The _____________ of a circle is the set of points inside the circle.Ex: Pt. _____

The _________________ is the point where the tangent and the circle intersect.Ex: Pt. _____

The _____________ of a circle is the set of points outside the circle.Ex: Pt. _____

A tangent line is _______________ to the radius of a circle drawn to the point of tangency. A line that is perpendicular to the radius of a circle at a point on the circle is a ______________________ __________ to the circle.

DY

CX

E

l

tA

D8 HW

1. Find the value of x to the nearest tenth.

a. b.

2. Find the value of x.

a. b.

3. Triangle ABC is circumscribed about circle G. Find:

a. x.

b. the perimeter of ABC.

30

G

J

20x

12H

A

C7 x

11B

6x - 4

Q

T

S

2x

Rx + 7

W

Z

Y

5x - 9

X

G

A

BC 17

14E

F

D27

2x

Angle Relationships in Circles

Intersections On or Inside a CircleIf a tangent or a secant intersects on a circle at the point of tangency then the angle formed is half the measure of its intercepted arc. ***Tangent BC and secant

BA intersect at B.

mABC = m

mABC = (150)

mABC = 75

If two secants or chords intersect in the interior of a circle, then the measure of the angle formed is half the sum of the measures of its intercepted arcs.

***Chords AB and CD intersect at E.

m1 = (m + m

)

m1 = (84 + 130)

m1 = (214)

m1 = 107

1. Find each measure.a. mQPR b. mQPS and mRPS

31

150

A

CB

CE1

D

B

A

130

84

148

QS

R

P

250

QS

R

P

c. mRQS if m = 238 d. m

e. m f. m

2. Find x.

a. b.

c. d.

32

Q

SR

T

64

D

C

F

E

116H J

KL

108

D C

BA

143

E

B

CA

Dx

75

116

H

G

KL

J

x

47

Q

M

75

P

N

x55

76

G

HE

F

x

88

e. f.

g. h.

D9 HW

Find each measure.

a. m3 b. mJMK c. m

33

L97 J

G

K H

x

110

154

Z

V

W

Y

x

128

62V

WU

Y

x96

25

K

LM

Jx

60

74

3

90

77

79H

K

JML

51

74N

Q

P

R

d. m e. mQPS f. mADB

If two segments intersect in the exterior of a circle, then the measure of the angle formed is half the difference of the measures of its intercepted arcs.

A Tangent and a Secant Two Tangents Two Secants

m1 = (m - m

)

m1 = (210 – 102)

= (108) = 54

m1 = 54

m2 = (m - m

)

m2 = (262 – 98)

= (164) = 82

m2 = 82

m3 = (m - m

)

m3 = (164 – 76)

= (88) = 44

m3 = 44

34

CB1A

D

102

210

LK3JM

N

76

164

E F2

HG

98

110

QS

R

P

72

D

C

F

E154D

CB

A

1. Find the value of x.

a. b.

c. d.

e. f.

g. h.

35

E Fx

G232

E Fx

G

142

U

T

179

R S71 x U

T

140

R

S74x

L

Q

75

P

M29 x N

HJ

G

K

26x

F

88

A

95

C

D56

x

B

224

Z

Y

68x

W

i. j.

k. l. Find mVTU

D10 HW

Find each measure.

1. mF 2. mS 3. mR

36

HJ

G

K

x25

F

110

L

Q

141

P

Mx 62 N

L

Q

108

P

Mx 35 N

S

U81

V

P

57

30

Q

R

T

E Fx

G

106

U

T

103

R S43 x

U

T

152

R

S88x

4. m 5. m

37

A

103

C

D41

x

B190

Z

Y

56x

W

Segment Relationships in Circles

Chord-Chord Product Theorem

If two chords intersect in the interior of a circle then the

38

A

CB9

4

E

D

6

x

Angle Relationships in Circles

Vertex lies _____ the circle.

Vertex lies __________ a circle.

Vertex lies __________ a circle.

Angle measure is half the measure of the intercepted

arc.

Angle measure is half the difference of the measures of the intercepted arcs.

Angle measure is half the sum of the measures of

the intercepted arcs.

X

Z

Y

85 A

C

D84

B

E

60

A

CB30

76

mXZY = (___)= ____

mAEB = mAEB =(___ + ___) = ____

mACB = (___ - ___) = ____

products of the lengths of the segments of the chords are equal.

AE EB = CE EDx 6 = 9 4

6x = 36x = 6

AE = 6

1. Find x.

a. b.

c. d.

e. f

39

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2. In circle O, chords AC and BD intersect at E. If EC = 8, BE = 9, and ED = 12, find AE.

D11 HWFind x. Round answers to the nearest tenth if necessary.

a. b. c.

d. e. f.

Segments Intersecting Outside the Circle

40

12 6x

510

6 x3

x + 5

x + 10

x + 20

x

U

T

124

R S44 x 68

G

HE

F

x

94

5x + 1

W

Z

Y

4x + 3

X

A secant segment is a segment of a secant with at least one endpoint on the circle.

An external secant segment is the part of the secant segment that lies in the exterior of the circle.

A tangent segment is a segment of a tangent with one endpoint on the circle.

If two segments intersect outside a circle, then the following theorems are true.Secant- Secant Product TheoremThe products of the lengths of one secant segment and its external segment equals the product of the lengths of the other secant segment and its external segment.

whole outside = whole outside AE BE = CE DE

Secant- Tangent Product TheoremThe products of the lengths the secant segment and its external segment equals the lengths of the tangent segment squared.

whole outside = tangent2

AE BE = DE2

41

A

EB

D

AE is a secant segment.

BE is an external secant segment.

ED is a tangent segment..

A

C

BE

D

AB

E

D

1. Find x.

a. b.

c. d.

e. f.

g. h.

42

G

L

x 8

K10

6J

HU

Rx

9

V4 5S

T

HEx

8

G

24

10

S

IF

E

x

5

C4.5

7.5A

D

B

Qx

8

S

12

P

RQ

4

6

S

x

P

R

G

x

4J

12

H

F

J4 x + 2

L

12

K

M

Segment Relationships in Circles

43

Q

S

R

X

Y

6

x

53

146

8

x

B

Z

F D

A

x

X

A

F

Y

12

4

Chords XY and QR intersect at S.

Secants AB and DB intersect at B.

Secant AY and tangent YX intersect at X.

p p = p pRS SQ = XS SY

O W = tan2

XF XA= XY2O W = O W

BZ BA = BF BD

___ ___ = ___ ______ = ___ ___ = ___SR = ___

___ ______ = ___ _____________ = ___

___ = ______ = ___ZA = ___

___ ___ = ______ = ______ = ___

XY = ___

D12 HW

Find each measure.

1. 2.

3. 4.

5. 6.

Equations of Circles

44

HE12

2

G

3

x

S

IF

E

10

7

Cx

5A

D

B

J5 x

L

9

K

M

J4 x

L

6

K

M

J7 x

L

14

K

M

E

8

4

Cx

3A

D

B

1. Write the equation of each circle.

a. a circle with center (5, 10) and radius 6

b. a circle with center (8, -4) and radius 3

c. a circle with center (-3, 12) and radius 5

d. a circle with center (-7, -8) and radius

e. a circle with center (0, 15) and radius 2.5

f. a circle with center (18, 0) and radius 10

g. a circle with center (0, 0) and radius 9

Identify the center and the radius from the equation.

45

Circles in the Coordinate

Plane

EquationThe equation of a circle with center (h, k) and radius r is

(x – h)2 + (y – k)2 = r2

(h, k) is the __________ of the circle, r is the __________ of the circle, and (x, y) is a __________ on the circle.

GraphExample

What is the equation of a circle whose center is (2, -3) and has a radius of 2?

(x – h)2 + (y – k)2 = r2

(x – 2)2 + (y – (-3))2 = 22

(x – 2)2 + (y + 3)2 = 4

xy

y

xy

y

xy

y

Given the equation (x – 1)2 + (y + 4)2 = 9, state the center and the radius.

(x – h)2 + (y – k)2 = r2

(x – 1)2 + (y + 4)2 = 9

(x – 1)2 + (y – (- 4))2 = 32

Therefore, center = (1, -4) and the radius = 3.*****Shortcut to get the center of the circle take the numbers out and change the signs.

2. For each equation, state the center and the radius of the circle.

a. (x - 6)2 + ( y – 4)2 = 25

b. (x - 3)2 + ( y – 7)2 = 16

c. (x + 4)2 + ( y – 5)2 = 36

d. (x + 1)2 + ( y – 5)2 = 14

e. x2 + ( y – 2)2 = 20

f. (x + 12) + y2 = 1

g. x2 + y2 = 12

3. Graph each circle.

a. a circle with center (-1, 3) and radius 9

b. (x + 2)2 + ( y – 3)2 = 25

center = _______

46

xy

y

radius = _____

c. (x - 4)2 + y2 = 9

center = _______

radius = _____

D13 HW

1. Write the equation of each circle.

47

xy

y

a. a circle with center (1, 3) and radius 8

b. a circle with center (2, -5) and radius 1

c. a circle with center (0, 15) and radius 11

d. a circle with center (-9, -4) and radius

2. For each equation, state the center and the radius of the circle.

a. (x - 8)2 + ( y – 1)2 = 144

b. (x - 3)2 + y2 = 36

c. (x + 4)2 + ( y – 6)2 = 81

d. (x + 7)2 + ( y + 7)2 =100

4. Graph each circle.

a. a circle with center (3, -4) and radius 4

You can also write the equation of a circle when you know the center and one point on the circle.

To write the equation of the circle,

48

xy

y

Use the distance formula to find the radius. Write the equation of the circle.

1. Write the equation of circle L that has center L(3, 7) and passes through (1,7).

2. Write the equation of circle B that has center (5, 4) and passes through (-3,4).

3. Graph and write the equation of the circle with a center (-2, 4) and passes through point (-6, 7).

If the diameter of a circle is perpendicular to a chord, it __________ the chord.

3. In circle O, diameter AOB chord CD at E. If CD = 16, find the length of CE.

49

B

D

A

C EO

4. Find x.

a. b.

5. In circle F, diameter DFE chord AC at B. Find the length of BF.

6. In circle O, diameter MON chord QR at T. If MN = 34 and QR = 30, find the length of OT.

50

2 7

x x

10

x2

2.5

4.8

D

A C2.5

B

E

F

N

R

M

Q TO