6.6 Secants, Tangents, and Chord Lengths
A
X
C
XA is a tangent segment
XB is a secant segment
XC is an external secant segment
BC is a chord
B
A
Theorems:
X
If two tangents intersect at the same
external point, then they are congruent.
 tangent length = tangent length
C
A
X
B
D
B
XA = XB
If two secants intersect outside a circle,
the product of the lengths of one secant
segment and its external segment equals
the product of the length of the other
secant segment and its external
segment.
XA*XC = XB*XD
 _______*______ =
______*_______
 This formula is “painful” to
remember! (_________)
 Or, it is an amazing formula!
(_________)
If a secant and a tangent intersect
outside a circle, then the product of
the length of the secant segment and
it’s external segment equals the length
of the tangent segment squared.
 _______ * _____ = (tangent length)2
A
C
X
D
B
AX * XB = CX * XD
A
X
B
D
XB  XD = AX 2
If two chords intersect inside a circle,
then the product of the lengths of the
segments of one chord equal the
product of the lengths of the segments
of the other chord.
 _____  _____ = ______  ______
Solve for x:
x
21
x
5
10
15
x
4
5
10 12
x
6