Segment Relationships in Circles - Pearland High School

Name: Lido

Notes-14.4

Date:

Segment Relationships in Circles

Period:

Chord --Chord Theorem

If two chords intersect inside a circle, then the roductS

of the lengths c

of the segments of the chords are equal.

D

EX 1: Find the value of x and the length of each chord.

a) c

6

3

CE?ED = BE

b)

1 HG.?J=kG

61

9

x

x E2

D

K68

12: x

-a part of a secant line with at least one point on the circle.

Secant --Secant Product Theorem

If two secants intersect in the exterior of a circle, then the product

of the lengths of one secant segment and its external segment

equals the product of the lengths of the other secant segment and

its external segment.

CEDE =

c

EX 2: Find the value of x and the length of each secant segment

a)

xc

b)

Ch'bR

5

6

6

72 = osx

8

S x

RP = (JPeTP

14?62

6

p

7

Name:

Notes-14.4

Date:

Period:

- a segment of a tangent line with exactly one endpoint on the circle.

Secant --Tangent Theorem

If a secant and a tangent intersect in the exterior of a circle, then the

product of the lengths of the secant segment and its external segment

Dic equals the length of the tangent segment squared. AC ??c

c

EX 3: Find the value of x.

a)

5c

2

x

(2+x)2 = g 2

b)

6

c hC?BC =DCt

x

Practice Problems: 1. Given AD = 12. Find the Value of x and the length of egch chord.

14

x c

3. Find the value of the variable.

2. Find the value of x and the length of each secant segment.

5.4

5

4S

x

5

c

2

x

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