ObjectiveAfter studying this section, you will be able to begin solving problems involving circles

9.2 Introduction to Circles

Find the circumference and the area of circle O.

O7 in

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. The red portion of the figure below is called arc CD (symbolized as CD).Arcs are measured in degrees. The length of an arc is a fraction of a circle’s circumference measured in linear units.

CD

Find the measure and the length of arc AB.

B (6,0)

A (0,6)

A sector of a circle is a region bounded by two radii and an arc of the circle.

Find the area sector CAT C

TA

906 in

A chord is a line segment joining two points on a circle. (A diameter is a chord passing through the center of a circle).

An inscribed angle is an angle whose vertex is on a circle and whose sides are determined by two chords of a circle.

C

B

A

Angle BAC intercepts arc BC

1. Find the circumference and the area of circle P.

P2.7

2. Given: Diagram as markedFind: a. measure of arc AB

b. The length of arc AB

B (8,0)

A (0,8)

3. Find the area of the shaded region. (Sector PAR)R(0,1

2)

A P(12,0)

4. Harry looked ahead to chapter 10 and discovered that the measure of an inscribed angle is half the measure of its intercepted arc. Use this information to find the measure of the inscribed angle DEF.

F

D

E

80

5. If HJ is a diameter of circle O, what are the coordinates of point O?

O

J (8,5)

H (-4,-3)

6. Show that triangle INS is a right triangle by:a. Finding the measure of angle INSb. Finding the slopes of IN and NS

S (10,0)

N (6,8)

I (-10,0)

7. Reflect point H over the y-axis to H’. Then find the slope of TH’

H (4,9)

T (10,2)

SummaryWhat did you learn about circles? How will this knowledge help you solve problems involving circles?

Homework: Worksheet 9.2