1. In the diagram of C, QR = ST = 16. Find CU.
EXAMPLE 4
Use Theorem 10.6
In the diagram of C, QR = ST = 16. Find CU.
SOLUTION
Chords QR and ST are congruent, so by Theorem 10.6 they are equidistant from C. Therefore, CU = CV.
CU = CV
Use Theorem 10.6.
2x = 5x – 9
Substitute.
x = 3
Solve for x.
So, CU = 2x = 2(3) = 6.

2. GUIDED PRACTICE for Example 4
In the diagram in Example 4, suppose ST = 32, and CU = CV = 12. Find the given length.
6. QR
SOLUTION
Since CU = CV. Therefore Chords QR and ST are equidistant from center and from theorem 10.6 QR is congruent to ST
QR = ST
Use Theorem 10.6.
QR = 32
Substitute.

3. GUIDED PRACTICE for Example 4
In the diagram in Example 4, suppose ST = 32, and CU = CV = 12. Find the given length.
7. QU
SOLUTION
Since CU is the line drawn from the center of the circle to the chord QR it will bisect the chord. 2
So QU = QR 1 2
So QU = (32) 1
Substitute.
QU = 16

4. GUIDED PRACTICE
for Example 4
In the diagram in Example 4, suppose ST = 32, and CU = CV = 12. Find the given length. 8.
The radius of C
SOLUTION
Join the points Q and C Now QUC is right angled triangle. Use the Pythagorean Theorem to find the QC which will represent the radius of the C

5. GUIDED PRACTICE for Example 4
In the diagram in Example 4, suppose ST = 32, and CU = CV = 12. Find the given length. 8.
The radius of C
SOLUTION
So QC2 = QU2 + CU2
By Pythagoras Theorem
So QC2 =
Substitute
So QC2 =
Square
So QC2 = 400
Add
So QC = 20
Simplify
ANSWER
The radius of C = 20