brain buster

1. Draw a circle with r = 4 and center A.

2. What is the diameter of the circle?

3. Explain the difference between a secant & a chord4. What do you know about a tangent line and the radius drawn to the point of tangency?

Math II

UNIT QUESTION: What special properties are found with the parts of a circle?Standard: MM2G1, MM2G2

Today’s Question:How do we use angle measures to find measures of arcs?Standard: MM2G3.a,d

P

A

BC

Central Angle : An Angle whose vertex is at the center of the

circleMinor ArcMajor Arc

Less than 180°

More than 180°

ABACB

To name: use 2 letters

To name: use 3 letters

APB is a Central Angle

P

E

F

D

Semicircle: An Arc that equals 180°

EDF

To name: use 3 letters

THINGS TO KNOW AND REMEMBER ALWAYS

A circle has 360 degrees

A semicircle has 180 degrees

Vertical Angles are Equal

measure of an arc = measure of central angle

A

B

C

Q 96

m AB

m ACB

m AE

E

=

=

=

96°

264°

84°

Arc Addition PostulateA

B

C

m ABC =

m AB + m BC

Tell me the measure of the following arcs.

80100

40

140A

B

C

D

R

m DAB =

m BCA =

240

260

Congruent Arcs have the same measure and MUST come from the same circle or of congruent circles.

4545

A

BC

D

110

A

B

C

D

In the same circle, or in congruent circles, two minor arcs are congruent

if and only if their corresponding chords are congruent.

AB CD IFF AB DC

120 120

60

x

x = 60

Ex. 1

2x x + 40

2x = x + 40

x = 40

Ex. 2

A

B

C

D

What can you tell me about segment AC if you know it is the perpendicular bisectors of segments DB?

It’s the DIAMETER!!!

Ex. 3 If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc.

y24

x

60x = 24

y = 30

Example 4EX 2: In P, if PM AT, PT = 10, and PM = 8, find AT.

T

AM

P

MT = 6AT = 12

Example 5In R, XY = 30, RX = 17, and RZ XY.

Find RZ.

R

X

Z

Y

RZ = 8

Example 6 IN Q, KL LZ. IF CK = 2X + 3 and CZ = 4x, find x.

K

Q

C

L

Zx = 1.5

In the same circle or in congruent circles, two chords are congruent if

and only if they are equidistant from the center.

A

B

C

D

M

L

P

AD BC

IFF

LP PM

Ex. 7: In A, PR = 2x + 5 and QR = 3x –27. Find x.

P

R

Q

A

x = 32

Ex. 8: IN K, K is the midpoint of RE. If TY = -3x + 56 and US = 4x, find x.

Y

T

S

K

x = 8

U

R

E