Rules for Dealing with Chords,
Secants, Tangents in Circles
Intersecting Chords:
If two chords intersect in a circle, the product of
the lengths of the segments of one chord equal
the product of the segments of the other
a b c d
(segment part) • (segment part) = (segment part) • (segment part)
Ex. 1: Finding Segment Lengths
S
• Chords ST and PQ
intersect inside the
circle. Find the
value of x.
Q
9
3
R
X
6
T
RQ • RP = RS • RT
9•x=3•6
9x = 18
x=2
P
Secant-Secant:
If two secant segments are drawn to a circle from
the same external point, the product of the length
of one secant segment and its external part is
equal to the product of the length of the other
secant segment and its external part.
a b c d
(whole secant) • (external part) = (whole secant) • (external part)
Ex. 2: Finding Segment Lengths
• Find the value of x.
Q
P
11
9
R
RP • RQ = RS • RT
10
S
x
9•(11 + 9)=10•(x + 10)
180 = 10x + 100
80 = 10x
8 =x
T
Secant-Tangent:
If a secant segment and tangent segment are
drawn to a circle from the same external point, the
product of the length of the secant segment and its
external part equals the square of the length of the
tangent segment
b c a
(whole secant) • (external part) = (tangent segment)2
2
Example:
In the figure if AD
9 cm, and AC
AB
B
x
x
2
C
D
25 cm
9 cm
AD AC
2
x
25 cm. Find x.
9 25
2
225
A
x
225 15 cm
Tangent-Tangent:
If two tangent segments are drawn to a circle from
the same external point, the lengths of the tangent
segments are equal.
B
a
a b
A
C
b
Example:
In the figure if AC
AB AC
x 9 cm
B
x
A
C
9 cm
9 cm, and Find x.
Intersecting Chords:
a b c d
Secant-Secant:
a b c d
Secant-Tangent:
b c a
Tangent-Tangent:
a
b
a b
2