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Daily Check. Homework Review. How do you know when two chords are congruent?. corresponding arcs are congruent. B. A. M. P. b. equidistant from the center. L. C. LP  PM ALP = BMP = 90. D. Flow Chart Proof. 2x. x + 40. 2x = x + 40 x = 40.

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How do you know when two chords are congruent?

  • corresponding arcs are congruent

B

A

M

P

b. equidistant from the center

L

C

LP  PM

ALP = BMP = 90

D



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

U

T

x = 8

TY = 32

K

E

R

S

Y


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

D

It’s the DIAMETER!!!

Arcs DC and BC are congruent!!!

A

C

B


IN Q, KL  LZ. IF CK = 2X + 3 and

CZ = 4x, find x.

Q

x = 1.5

C

Z

K

L


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

P

A

M

MT = 6

T

AT = 12


Your turn
Your turn!

ÐUTV ÐXTW.

Find WX.___________

130º

11

Find ___________


Your turn1
Your turn!

Find the length of each chord.

96

30

LN = _______

CE = _______


Segment Lengths in Circles

  • Find the lengths of segments of chords

  • Find the lengths of segments of tangents and secants


Secant and Tangent

2 Secants intersecet outside

Chords intersect inside


Two chords intersect

INSIDE the circle

Type 1:

a

ab = cd

d

c

b


Solve for x.

9

6

x

x = 3

2


Find the length of db

12

2x

8

3x

Find the length of DB.

x = 4

DB = 20

A

D

C

B


Find the length of each chord
Find the length of each chord.

D

x = 8

AC = 13

DB = 14

A

x - 4

x

C

5

10

B


Two secants intersect

OUTSIDE the circle

Type 2:

E

A

B

C

D

EA•EB = EC•ED


Ex: 3 Solve for x.

B

13

A

7

E

4

C

x

D

7

(7 + 13)

=

4

(4 + x)

x = 31

140 = 16 + 4x

124 = 4x


Ex: 4 Solve for x.

B

x

A

5

D

8

6

C

E

6

(6 + 8)

=

5

(5 + x)

84 = 25 + 5x

x = 11.8

59 = 5x


Type 2 (with a twist):

Secant and Tangent

C

B

E

A

EA2= EB • EC


Ex: 5 Solve for x.

C

B

x

12

E

24

A

(12 + x)

242

=

12

x = 36

576 = 144 + 12x


Ex: 6

5

B

E

15

C

x

A

(5 + 15)

x2

=

5

x2 = 100

x = 10


Homework

Practice Worksheet


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