1. Circles: The Length of Tangent/Secant Lines
Endpoint outside the circle…

2. Secant and Tangent Lines
If part of secant line is outside circle, call it the “external segment.” A
DA = Secant Line
DC = Tangent Line
DB = External Segment of the Secant Line. B D C

3. Secant and Tangent Lines
The square of the tangent line is equal to the product of the external segment and the whole secant line.
(Tangent)2 = External Segment(Secant Line) A
(DC)2 = DB(DA) B D C

4. Example 8 x Secant: DA = 20 Ext. Seg: DB = 8 (DC)2 = DB(DA)
To find an unknown length: Use a variable.
Substitute the values you know.
Simplify.
Secant: DA = 20
Ext. Seg: DB = 8 A
(DC)2 = DB(DA) B 8
(x)2 = 8(20) D x C