Section 7.6: Circles and Arcs

Section 7.7: Areas of Circles, Sectors, and Segments

Section 7.8: Geometric Probability

Review of Circles

Formulas:

Area A = r2

Circumference C = 2r = d

= 3.141592654 . . . (on a scientific calculator)

Most people use = 3.14

You name a circle by its

center point: circle P

P

C

D

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.

CD

symbol

Arcs (parts of circles)

Semi-circle: half

Minor arc < semicircle

Major arc > semi circle

CD

DCX

X

CX

A central angle is an angle whose vertex is the center of the circle.

EF

L120

angle. central a is ELF

Measure of Arc AB (degrees) = measure of the central angle

Length of Arc AB (partial circumference)

πd360

Angle Central

EF

L120

EF=120

6 cm

DC

P

A

B

Identify at least one minor arcs, at least one major arcs, and both semi-circles in Circle P.

Find the measure of arc RS, the length of arc SR (in terms of ), and the length of arc SQR (in terms of π).

SR

O

Q

320

12 cm

Sectors

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.

A (0, 8)

B (8, 0)

X (0, 0)

2πr360

Angle) (CentralArea Sector

2

2

u 16π

π836090

SectorAXB

Find the area of shaded sector ACB in terms of .

A

B

C

1006 cm

ChordsA 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.

Q

S

R

The measure of an inscribed angle is half the measure of its intercepted arc.

EF

L120 24 ft

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.

Find the area of shaded segment, in terms of , then rounded to the nearest tenth.

EF

L120 4 ft

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

10 in

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

60

13 cm

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

90

22 in

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

7 m

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?

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 135. Express your answer in terms of .

Homework

7.6-7.7 Walsh Worksheet