http://www.ck12.org Chapter 9. Circles
Tangent Secant Segment Theorem: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 A
Find the value of the missing segment.
Use the Tangent Secant Segment Theorem. Square the tangent and set it equal to the outer part times the whole
secant.
x^2 = 4 ( 4 + 12 )
x^2 = 4 · 16 = 64
x= 8Example B
Find the value of the missing segment.
Use the Tangent Secant Segment Theorem. Square the tangent and set it equal to the outer part times the whole
secant.
202 =y(y+ 30 )
400 =y^2 + 30 y
0 =y^2 + 30 y− 400
0 = (y+ 40 )(y− 10 )
y=− 40 HHH , 10