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Homework Review

How do you know when two chords are congruent?

LP PM

ALP = BMP = 90

a. corresponding arcs are

congruentA

B

C

D

M

L

P AD BC

b. equidistant from the center

Flow Chart Proof

AB CD

Given

EA EB EC ED

All radii are congruent

AEB CED

Congruent arcs have

congruent measures

AEB CED

SAS

AB CD

CPCTC

2x x + 40

2x = x + 40

x = 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

R

E

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!

ÐUTV ÐXTW.

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

6

xx = 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

x

5

x - 4

10

A

B

C

D

E A B

C

D

EA • EB = EC • EDoutside whole = outside whole

EA

B

C

D

713

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

C

15

5

x

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

x2 = 100

x = 10

Ex: 6