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"