Obj. 59 Segment Relationships

The student is able to (I can):

• Find the lengths of segments formed by lines that intersect circles

chord-chord product

If two chords intersect in the interior of a circle, then the products of the lengths of the segments of the chords are equal.

S

P

A

CE

AA PS AC EA=i i

Example 1. Find the value of x.

2. What is the diameter of the circle?

9 12

x6 ( )=9x 6 12=9x 72

6

6

=x 8

( )=4x 6 6=4x 36=x 9

= + =diameter 4 9 134

x•

secant-secant product

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.

(whole • outside = whole • outside)

O

P

ME

TPM MT EM OM=i i

Example Find the value of x.

10x

812

( ) ( )+ =10 x 10 12 20

+ =10x 100 240

=10x 140=x 14

secant-tangent product

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 equals the length of the tangent segment squared.

(whole • outside = tangent2)

G

OR

F

2FO RO GO=i

Example Find the value of x.

810

x

( )+ =210 8 8 x

( )( ) =218 8 x

=2144 x

=x 12