9.6. Segments of Chords, Secants, and Tangents http://www.ck12.org
Segments from Secants and Tangents
If a tangent and secant meet at a common point outside a circle, the segments created have a similar relationship to
that of two secant rays in Example 3. Recall that the product of the outer portion of a secant and the whole is equal
to the same of the other secant. If one of these segments is a tangent, it will still be the product of the outer portion
and the whole. However, for a tangent line, the outer portion and the whole are equal.
Theorem 9-16:If a tangent and a secant are drawn from a common point outside the circle (and the segments are
labeled like the picture to the left), thena^2 =b(b+c).
This means that the product of the outside segment of the secant and the whole is equal to the square of the tangent
segment.
Example 4:Find the value of the missing segment.
a)
b)
Solution:Use Theorem 9-16. Square the tangent and set it equal to the outer part times the whole secant.
a)x^2 = 4 ( 4 + 12 )
x^2 = 4 · 16 = 64
x= 8
b) 20^2 =y(y+ 30 )
400 =y^2 + 30 y
0 =y^2 + 30 y− 400