CK-12 Geometry Concepts

9.10. Segments from Secants http://www.ck12.org

Use the Two Secants Segments Theorem to set up an equation. For both secants, you multiply the outer portion of
the secant by the whole.

18 ·( 18 +x) = 16 ·( 16 + 24 )

324 + 18 x= 256 + 384

18 x= 316

x= 17

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Example B

Find the value of the missing variable.

Use the Two Secants Segments Theorem to set up an equation. For both secants, you multiply the outer portion of
the secant by the whole.

x·(x+x) = 9 · 32

2 x^2 = 288

x^2 = 144

x= 12

x 6 =−12 because length cannot be negative.

Example C

True or False: Two secants will always intersect outside of a circle.

This is false. If the two secants are parallel, they will never intersect. It’s also possible for two secants to intersect
inside a circle.

Watch this video for help with the Examples above.

MEDIA

Click image to the left for more content.

CK-12 Foundation: Chapter9SegmentsfromSecantsB

Concept Problem Revisited

The given information is to the left. Let’s set up an equation using the Two Secants Segments Theorem.