# 10 Circles

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O IS THE CENTER OF THE CIRCLE OBCD IS A RECTANGLE AB=3 BD=5

O IS THE CENTER OF THE CIRCLE, OBCD IS A RECTANGLE AB=3 BD=5FIND THE RADIUS OF THE CIRCLE

O IS THE CENTER OF THE CIRCLE Find AEGIVEN: (O; ;

Chords are equidistant from the center of (O PROVE: (

GIVEN: (O;

SYMBOL 208 \f "Symbol"PBMSYMBOL 64 \f "Symbol"

SYMBOL 208 \f "Symbol"AMBPROVE:

(O

bisects

BT=8RT=BP=2Find ST and AO

Given (O, BC=5, PQ=30

Find the radius of (O

Given (O with radius 12 and AB=12; Find OP(O has radius 12. How far from the center of the circle is a chord with length 12?

are tangentsAB=30; BC=20; DC=14 Find AD

(O has radius 10(P has radius 7(O is tangent to (P

is tangent to both Find the length of

THE WALKAROUND PROBLEMFN=20; NU=14, FU=12(F,(U, & (N are tangent to each other.Find the radii of all three circles.

THE COMMON EXTERNAL TANGENT PROBLEMThe radius of (E=12. The radius of (A=8. EA=40

is tangent to both circles. Find its lengthTHE COMMON INTERNAL TANGENT PROBLEM

is tangent to (A and (H. HA=40The radius of (A is 8The radius of (H is 12Find RDTwo circles with radii 8 and 4 are externally tangent. Find the length of the common tangent segment.

(C,(U &( B are tangent.CU=28CB=22BU=25Find the radius of (C

is a diameterm(A=30(AB=13GD=1Find CD and EA.

Given Semicircle W,TA=4, ST = 6

Find the diameter of the semicircle.

(O has radius 12, (S has radius 9OS=28Find the length of the external and internal common tangent segments to the two circles.

is tangent to both (s.The radius of (A=4The radius of (B=9Find SM

SYMBOL 68 \f "Symbol"PQR is equilateralIts sides are tangent to the sides of the smaller of the two concentric circles. If the radius of the larger circle is 12, find the radius of the smaller circle.mSYMBOL 208 \f "Symbol"GKD = 80SYMBOL 176 \f "Symbol"; mSYMBOL 208 \f "Symbol"R=32SYMBOL 176 \f "Symbol"; Find the measure of all arcs and angles in the diagram

BIG CIRCLE

is tangent to (O at F

IKMJ is a parallelogram JM = 8 ; JI = 10 Find the diameter of the circle

is a diameter of the circle AB = 12

(

Find the diameter of the circle and the measure of all arcs.Find any other thing you can. Can you determine EF?Square ABCD has side length 2. A semicircle with diameter is constructed inside the square., and the tangent to the semicircle from C intersects side at E. What is the length of ?

Circles A,B and C are externally tangent to each other and internally tangent to circle D. Circles B and C are congruent. Circle A has radius 1 and passes through the center of D. What is the radius of circle B?

is a diameter; AB = 12; ;

Find BC, DC, DB & DE(ABC is drawn in a circle so is a diameter and (CAB=60(. B is on the circle. AB = 10. Find the diameter of the circle and the length of

A regular hexagon is inscribed in a circle. Each side of the hexagon is 6. Find the diameter of the circle and the distance from the center of the circle to one edge of the hexagon.A regular octagon is inscribed in a circle. Each side of the octagon is 8. Find the diameter of the circle and the distance from the center of the circle to one edge of the octagon.A regular decagon is named . Find each angle

Diagonals and intersect at BFind

The endpoints of the diameter of a circle are the x and y intercepts of the line with equation . Find the radius of the circle and decide if the circle passes through the origin.

is tangent to the circle

; AB=16The radius of the circle is 10Find CD, BD

O is the center of both and

; AC=8The length of = the length of

Find the length of

(ABC is equilateral, cm.Find the length of

m(PAC=90(A is the centerPA=8Find the total perimeter of the figure

The curved pieces on either end are semicircles. Find the total perimeter.PQ=24

is a diameter of (O

is tangent to (O at Pm(QPR=30(PS=PR=RS=

Find m(N and m(LThe two circles are concentric with center O. is tangent to the smaller circle. The radii of the two circles are 6 and 12. Determine the length of

The two circles are concentric with center O. is tangent to the smaller circle at P. Find the length of

(A & (B are externally tangent. is the common internal tangentThe radius of (A is 8.The radius of (B is 2Find CE,DF,BD,DA,m(CFE (draw it in ) m(ADB and CF

The circles are concentric and are inscribed in squares. AB=16Find the circumference of the smallest circle picturedPOWER

TM=3MW=4

MS=12Find PMSYMBOL 231 \f "Wingdings"SYMBOL 232 \f "Wingdings"

is tangent FT=8 ;KT=6Find RTSYMBOL 232 \f "Wingdings"

BC=8DC=6AB=4Find ED

KW=KM=6NR=1Find RW

Determine x,y,z,w,s and m

Please do these problems in numerical order.

Prove Davids Theorem Given: (O,(P

tangent to (P

tangent to (OProve: bisects (AOK

STATEMENTS(REASONS

(

(

(

(

(

(

(

(

(

(

(

(

(

Given: are each tangent to two circles(A is tangent to (B at D(A is tangent to (C at F(B is tangent to (C at EProve:(ABC is equilateral

STATEMENTS(REASONS

(

(

(

(

(

(

(

(

(

(

(

(D

C

E

A

B

D

B

C

A

EMBED Word.Picture.8

EMBED Word.Picture.8

EMBED Word.Picture.8

EMBED Word.Picture.8

EMBED Word.Picture.8

C

B

P

F

E

D

O

Q

C

B

P

S

T

O

EMBED Word.Picture.8

A

B

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B

G

C

A

E

D

F

_1330325134.unknown

_1330325199.doc

C

D

E

F

B

A

_1330325194.doc

3

EMBED Equation

Find m(R

5.(O, EMBED Equation EMBED Equation

Find m(M,m(R and m(MST

100(

40(

R

L

S

T

M

4.(O, EMBED Equation EMBED Equation Find m(D,m(F,m(DHE

E

D

F

G

H

60(

80(

B

6 Find m(C and m(FRW

R

P

W

F

J

C

30(

80(

S

Q

R

50(

2.(O

EMBED Equation

Find m(S

1. (O

m EMBED Equation

Find m(CAB

80(

O

O

P

T

S

120(

C

A

O

x

_1330325195.doc

A

B

K

C

P

O

_1330325193.doc

m

104(

88(

s

52(

88(

114(

48(

w

38(

26(

z

y

23(

x

58(

_1330325183.unknown

_1330325186.doc

B

A

F

E

D

C

_1330325184.unknown

_1330325181.unknown

_1330325182.unknown

_1330325180.unknown

_1330325179.doc

80(

120(

L

N

U

V

_1330325175.doc

20

20

12

_1330325176.doc

O

S

R

Q

P

_1330325174.doc

EMBED Equation

P

C

A

_1330325171.doc

B

C

A

_1330325144.unknown

_1330325145.unknown

_1330325143.unknown

_1330325138.doc

C

F

D

E

B

A

G

_1330325133.unknown

_1330325108.doc

T

A

B

M

S

_1330325107.doc

D

S

O

C

B

A

_1330325105.doc

W

S

A

T

B

_1330325101.doc

B

U

C

_1330325099.unknown

_1330325096.unknown

_1330325097.unknown

_1330325092.unknown

_1330325093.unknown

_1330325089.unknown

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