NAME ______________________________________________ DATE

____________ PERIOD _____

10-7 Study Guide and Intervention Special Segments in a Circle Segments Intersecting Inside a Circle

If two chords intersect in a circle, then the products of the measures of the chords are equal.

d

b

a

O

c

a!b"c!d Example

Find x. The two chords intersect inside the circle, so the products AB ! BC and EB ! BD are equal. AB ! BC 6!x 6x x

" " " "

EB ! BD 8!3 24 4

D 3

A

6

x

C

B 8

E

Substitution Simplify.

AB ! BC " EB ! BD

Divide each side by 6.

Exercises Find x to the nearest tenth. 1.

2.

2

2

x

6

3

x Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

x 10

3.

4.

6 8

3

x 6

8

x!7

x

5.

6. 2

5

x

7

x!2

7.

8.

2x

3x

5

6

6

3x

Chapter 10

8

50

x

Glencoe Geometry

NAME ______________________________________________ DATE

10-7 Study Guide and Intervention

____________ PERIOD _____

(continued)

Special Segments in a Circle a circle, then two products are equal.

• If two secant segments are drawn to a circle from an exterior point, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment.

P

• If a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment. B

A

B C

If secants and tangents intersect outside

A C

D

D

Q

E AB ! ! is a tangent segment. !D A ! is a secant segment. ! AC ! is an external secant segment. (AB)2 ! AD " AC

AC ! ! and ! AE ! are secant segments. A !B ! and A !D ! are external secant segments. AC " AB ! AE " AD

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Example

Find x to the nearest tenth. The tangent segment is A !B !, the secant segment is ! BD !, and the external secant segment is B !C !. 2 (AB) ! BC " BD (18)2 ! 15(15 # x) 324 ! 225 # 15x 99 ! 15x 6.6 ! x

A

T

18

B 15

C

x

D

Exercises Find x to the nearest tenth. Assume segments that appear to be tangent are tangent. 1.

2.

3.3

16

2.2

x

4.

x

6

8

2

Y

x

11

9.

15

21 5

Chapter 10

6.

x!3

8.

35

2x

4x

5x

9

7.

6

W

6

V

x

5. 13

8

T

18

S

3.

26

8

x 6

x

51

Glencoe Geometry

Lesson 10-7

Segments Intersecting Outside a Circle