Prove All Circles are Similar

1  

1  

Circle Equations • Equation in standard form

(x – h)2 + (y – k)2 = r2 Center coordinates “use opposite sign”  

Make sure you square the radius!

• Writing Circle Equations 1) Need center -if this isn’t given, use midpoint formula

2) Need radius -if this isn’t given, use distance formula on center and one endpoint on circle

3) Substitute center and radius into the standard form of a circle equation

Write the standard equation of the circle with the following center and radius: 1. center (6, -2) r=7

2. center (-1, -3) r= 5

3. center (0, 0) r=3

Find the center and radius of each circle: 4. x2 + (y – 15)2 = 1

5. (x – 9)2 + (y + 1)2 = 81

6. (x – 4)2 + (y – 3)2 = 121

7. Write the equation of the circle with center (1, -3) that passes through the point (4, 2).

8. A diameter of a circle has endpoints (-3, 7) and (5, 5). Write an equation of the circle.

9.

Circles- Angle Formulas • Central Angles

∠

x = arc

 

• Inscribed Angles

 

∠x

=

1 arc 2

∠x

=

1 (arc1 + arc2) 2

• Angles formed by two chords

 

• Exterior Angles formed by secants and tangents

∠x  

=

1 (arc1 – arc2) 2  

Circles- Segment Formulas • Two Chords

ab = cd  

• Two Secants a(a + b) = c(c + d)  

• Secant and Tangent

a2 = b(b + c)    

Also….

10.

Find x.

m ∠ ABC = 32º

11.

Find m ∠ AOC.

220◦  

A  

C  

1   1  

O  

x  

B  

12.

BC is the diameter of circle O.

13.

Find mBD

Find mBEC D   A

◦  

1101   O  

B  

40

C  

D  

1    

 

O 50◦  

◦  

C  

B  

E  

14.

Find m ∠ AEB C   E  

B   70

1    

O

◦  

A  

15.

90◦  

Find m ∠ A

130◦  

B  

D   D  

1  

O  

  C   A

16.

In circle O, chord AB is parallel to diameter CD . If mAC = 40º, what is m ∠ CAB?

A  

B  

C  

17.

D  

O  

Chord AB ≅ chord BC . If m ∠ B = 52º, find m ∠ C. B  

A  

C  

18. x○  

O   50○  

mCD = 110º

19.

20.

Find m ∠ DCB D  

O

21.

Find m ∠ P E  

1  

A  

mTQ = 20º, mTS = 90º

S   T  

 

1  

R  

C  

Q  

O  

B  

Diameter CD ⊥ chord AB AB = 12 and CE = 9, find ED.

22.

AE = 6, CE = 4, and ED = 3 Find EB. C  

C  

B  

E   A  

1  

O  

A  

E   D  

B  

1  

D  

P  

23.

If PQ = 4, QR = 8, and PS = 3, find ST. R   Q   1  

P   S  

T  

24.

Diameter CD is extended to point A and tangent AB is drawn. If CO =12 and AB = 9, find AC. B  

25.

1  

C  

A  

O  

D  

If AD = 5, DB = 3, and BC = 16, find AC.

 

A   F  

D  

B  

E  

C