1. Section 7.6: Circles and Arcs
Section 7.7: Areas of Circles, Sectors, and Segments
Section 7.8: Geometric Probability

2. Review of Circles You name a circle by its center point: circle P
Formulas:
Area A = r2
Circumference C = 2r = d
 = (on a scientific calculator)
Most people use  = 3.14 P

3. Arcs (parts of circles)
An arc is made up of two points on a circle and all the points of the circle needed to connect those two points by a single path. X CD CX
Semi-circle: half
Minor arc < semicircle
Major arc > semi circle
symbol CD
DCX

4. A central angle is an angle whose vertex is the center of the circle.
120 L

5. EF=120 Measure of Arc AB (degrees) = measure of the central angle
Length of Arc AB (partial circumference) E F
6 cm
120 L

6. B A P C D
Identify at least one minor arcs, at least one major arcs, and both semi-circles in Circle P.

7. Q
320 O
12 cm R S
Find the measure of arc RS, the length of arc SR (in terms of ), and the length of arc SQR (in terms of π).

8. Sectors
A (0, 8)
A sector of a circle is a region bounded by two radii and an arc of a circle. The pink area shows sector AXB. A sector has an area.
B (8, 0)
X (0, 0)

9. Find the area of shaded sector ACB in terms of .
6 cm
100 A B
Find the area of shaded sector ACB in terms of .

10. Chords
A chord is a line segment joining two points on a circle. (A diameter is a special chord that passes through the circle center.) RQ and RS are chords.
An inscribed angle is an angle whose vertex is on a circle and whose sides are determined by two chords of the circle. QRS is an inscribed angle.
The measure of an inscribed angle is half the measure of its intercepted arc. Q S R

11. Segments
A segment of a circle is a region bounded by an arc and the chord having the same endpoints as the arc. The yellow area shows a segment. E F
120
24 ft L

12. Find the area of shaded segment, in terms of , then rounded to the nearest tenth.
120
4 ft L

13. Circle S has a diameter of 10 in and an inscribed square
Circle S has a diameter of 10 in and an inscribed square. Find the area of the shaded regions in terms of .
10 in S

14. Find the area of the shaded region. Round to the nearest whole number.
13 cm
60

15. Find the area of the shaded region. Round to the nearest whole number.
90

16. Find the area of the shaded region. Express your answer in terms of .

17. Geometric Probability
Instead of the ratio of favorable outcomes to total possibilities, compare the target area to the entire area.
d = 12 in
A dart lands on a random point on the circular target shown. What is the probability that it lands on the 3-in square bull’s-eye?

18. A park contains two circular playgrounds
A park contains two circular playgrounds. One has a diameter of 60 m and the other has a diameter of 40 m. How much greater is the area of the larger playground? (Round to the nearest whole number.)
A circle has an 8-in radius. Find the area of a sector whose arc measure is Express your answer in terms of .

19. Homework
Walsh Worksheet