1. Geometry
Section 10.3

2. Coins
You notice that the word LIBERTY on the heads side of a quarter makes about the same arc as the words QUARTER DOLLAR on the tails side. Explain how you can use a straight ruler to check whether this is true.

4. EXAMPLE 1
Use congruent chords to find an arc measure
In the diagram, P Q, FG JK , and mJK = 80o. Find mFG
SOLUTION
Because FG and JK are congruent chords in congruent circles, the corresponding minor arcs FG and JK are congruent.
So, mFG = mJK = 80o.

6. EXAMPLE 2
Use perpendicular bisectors
Three bushes are arranged in a garden as shown. Where should you place a sprinkler so that it is the same distance from each bush?
Gardening
SOLUTION
STEP 1
Label the bushes A, B, and C, as shown. Draw segments AB and BC .

7. EXAMPLE 2
Use perpendicular bisectors
STEP 2
Draw the perpendicular bisectors of AB and BC By Theorem 10.4, these are diameters of the circle containing A, B, and C.
STEP 3
Find the point where these bisectors intersect. This is the center of the circle through A, B, and C, and so it is equidistant from each point.

8. EXAMPLE 3
Use a diameter
Use the diagram of E to find the length of AC . Tell what theorem you use.
SOLUTION
Diameter BD is perpendicular to AC . So, by Theorem 10.5, BD bisects AC , and CF = AF. Therefore, AC = 2 AF = 2(7) = 14.

10. 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.