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Homework Review

UNIT QUESTION: What special properties are found with the parts of a circle?Standard: MMC9-12.G.C.1-5,G.GMD.1-3

Today’s Question:How can I find a segment length for a piece of a chord?Standard: MMC9-12.G.C.2

GPS GeometryDay 25 (9-11-13)

How do you know when two chords are congruent?

LP PMALP = BMP = 90

a. corresponding arcs are

congruentA

B

C

D

M

L

P AD BC

b. equidistant from the center

Flow Chart Proof

AB CDGiven

EA EB EC EDAll radii are congruent

AEB CEDCongruent arcs havecongruent measures

AEB CEDSAS

AB CDCPCTC

2x x + 40

2x = x + 40x = 40

In K, K is the midpoint of RE. If TY = -3x + 56 and US = 4x, find the length of TY.

Y

T

S

Kx = 8

TY = 32

U

RE

A

B

C

D

IF AC is the perpendicular bisector of segment DB, then…

It’s the DIAMETER!!!Arcs DC and BC are congruent!!!

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

K

Q

C

L

Zx = 1.5

In P, if PM AT, PT = 10, and PM = 8, find AT.

T

AM

P

MT = 6AT = 12

Your turn!

UTV XTW.

Find WX.___________ Find ___________mAB11 130º

Your turn! Find the length of each chord.

CE = _______ LN = _______30 96

Segment Lengths in Circles

Find the lengths of segments of chords

Find the lengths of segments of tangents and secants

a

bc

d ab = cd

part part = part part

9

2

6xx = 3

Solve for x.

Find the length of DB.

8

12

2x

3x

x = 4

DB = 20

A

B

C

D

Find the length of each chord.

x = 8

AC = 13

DB = 14

x5

x - 4

10

A

B

C

D

E A B

C

D

EA • EB = EC • EDoutside whole = outside whole

EA

B

C

D

7 13

4

x

7 (7 + 13) 4(4 + x)=

Ex: 3 Solve for x.

140 = 16 + 4x124 = 4x

x = 31

E

A

B

CD 8

5

6

x

6 (6 + 8) 5(5 + x)=

Ex: 4 Solve for x.

84 = 25 + 5x59 = 5x x = 11.8

E

A

B C

EA2 = EB • ECoutside whole = outside whole

E

A

B C

24

12 x

outside whole = outside whole 242 = 12 (12 + x)576 = 144 + 12x x = 36

Ex: 5 Solve for x.

E

A

B

C15

5

x

outside whole = outside whole x2 = 5 (5 + 15)

x2 = 100x = 10

Ex: 6