Name:_____________________
Notes 9.6 Find Segment Lengths in Circles
Segments of a chord ________________________________________________________________________
__________________________________________________________________________________________
Secant segment ____________________________________________________________________________
__________________________________________________________________________________________
External segment __________________________________________________________________________
THEOREM 10.14: 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.
EA • ________ = EC • ________
Example 1: Find lengths using theorem 10.14
Find ML and JK.
THEOREM 10.15: 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.
EA • ______ = EC • ______
Example 2: Use Theorem 10.15
Find the value of x.
Checkpoint Find the value of x.
1.
2.
THEOREM 10.16: 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.
EA2 = _______ • _______
Example 3: Find lengths using Theorem 10.16
Use the figure at the right to find RS.
Checkpoint Complete the following exercise.
3. Use the figure at the right to find JK.
Example 4: Solve a real-world problem
Fountain You are standing at point C, 45 feet from the Point State Park fountain
in Pittsburgh, PA. The distance from you to a point of tangency on the fountain is
105 feet. Find the distance CA between you and your friend at point A. What is
the radius of the fountain?