segments
of one
chord isshare
equalthe
to the
product
of
If
two secant
segments
same
endpoint
What is the external segment of DE?
the
lengths
of
the
segments
of
the
other
chord.
outside a circle, then the product of the lengths
of one secant segment and its external segment
________ = ________
equals the product of the lengths of the other
secant
segment
and itsLengths
external segment.
10.6
Find
Segment
in Circles +JMJ
1. Find x.
2. Find x.
4. Find x.
Name
two
5.
Find
x. secant segments.
SEGMENTS OF SECANTS THEOREM
If two secant segments share the same endpoint
outside a circle, then the product of the lengths
of one secant segment and its external segment
equals the product of the lengths of the other
Are
the
chordsand
equal
in length?
secant
segment
its external
segment.
What is the external segment of EB?
What is the external segment of DE?
Are the chords equal in length?
3. Ifthe
thesecant
chordssegments
were equal
in problem
#2. What could you conclude about arc US ?
Are
equal
in length?
4. Find x.
SEGMENTS OF SECANTS AND TANGENTS
THEOREM
If a secant segment and a tangent segment
share an endpoint outside a circle, then the
product of the lengths of the secant segment
and its external segment equals the square of
the length of the tangent segment.
What is the tangent
5. Find x.
segment?
What is the secant
segment?
What is the external segment of the secant
segment?
Are the secant segments equal in length?
6. Find x.
SEGMENTS OF SECANTS AND TANGENTS
THEOREM
If a secant segment and a tangent segment
share an endpoint outside a circle, then the
product of the lengths of the secant segment
and its external segment equals the square of
the length of the tangent segment.
6. Find x.
What
is the
tangent
7.
a) Find
the
length of the secant segment.
segment?
b) Find the length of the tangent segment.
What is the secant
segment?
What is the external segment of the secant
segment?
7. a) Find the length of the secant segment.
b) Find the length of the tangent segment.
Geometry Notes
10.6 Find Segment Lengths in Circles
Foldable:
Name ________________
Segments of the Chord: when two chords intersect in the
interior of a circle, each chord is divided into two segments
called segments of the chord.
Secant Segment: a secant segment is a segment that
contains a chord of a circle, and has exactly one endpoint
outside the circle.
External Segment
An external segment is the part of a secant segment that is
outside the circle.
Theorems
Picture/ Description
What are the segments of chord DC?
SEGMENTS OF CHORDS THEOREM
If two chords intersect in the interior of a
circle, then the product of the lengths of the
segments of one chord is equal to the product of
the lengths of the segments of the other chord.
What are the segments of chord AB?
________ = ________
1. Find x.
SEGMENTS OF SECANTS THEOREM
If two secant segments share the same endpoint
outside a circle, then the product of the lengths
of one secant segment and its external segment
equals the product of the lengths of the other
secant segment and its external segment.
Are the chords equal in length?
2. Find x.
Name two secant segments.
What is the external segment of EB?
What is the external segment of DE?
Are the chords equal in length?
3. If the chords were equal in problem #2. What could you conclude about arc US ?
4. Find x.
5. Find x.
Are the secant segments equal in length?
SEGMENTS OF SECANTS AND TANGENTS
THEOREM
If a secant segment and a tangent segment
share an endpoint outside a circle, then the
product of the lengths of the secant segment
and its external segment equals the square of
the length of the tangent segment.
6. Find x.
What is the tangent
segment?
What is the secant
segment?
What is the external segment of the secant
segment?
7. a) Find the length of the secant segment.
b) Find the length of the tangent segment.