10-1 Circles10-1 CirclesPage 697Page 697

• A circle is the set of all points in a plane that are a given distance from a given point in that plane. The given point is the center of the circle.

•

RadiusRadius• A radius of a circle is a segment that

has one endpoint at the center of the circle and the other endpoint on the circle.

ChordChord• A chord of a circle is a segment that

has its endpoints on the circle

DiameterDiameter• A diameter of a circle is a chord that

contains the center of the circle.• A diameter is twice as long as a

radius, or a radius is half as long as a diameter.

PiPi• Pi is an irrational number that is the

ratio of the circumference of a circle to its diameter.

• Л = 22/7 or 3.14

CircumferenceCircumference• The circumference of a circle is the

distance around the circle.• C = 2лr• C = dл

Example 1Example 1• Refer to the application at the

beginning of the lesson. The surveyor’s wheel has a diameter of 1.59 feet. What is the length of each spoke of the wheel?

Example 2Example 2• Find the circumference of a circle

with a radius of 6.8 centimeters.

Example 3Example 3

• In 1966, inspectors checked the accuracy of the Olympic marathon course by using the calibrated bicycle method. The inspectors rode bicycles equipped with counters that tracked the turns of the wheels. If the radius of a bicycle wheel is 13 inches and the counter shows 20,000 revolutions at the end of a course, how long is the course.

• C = 2лr• = 2л13inches• = 26л• =81.64

• 20,300 x 81.64 = 1657292 inches• 1657292/63360• = 26.1567• =26.2 miles

Example 4Example 4• Find the exact circumference of

circle p.• C2 = a2 + b2

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16

30

6. Name two chords.6. Name two chords.7. If AL = 9.4, find KD.7. If AL = 9.4, find KD.8. Is NO < AL? Explain.8. Is NO < AL? Explain.

9. r = 7 d = ____ c = ____9. r = 7 d = ____ c = ____10. c = 76.4 d = _____ r = ______10. c = 76.4 d = _____ r = ______

Find the circumference of circle T.Find the circumference of circle T.

• Assignment• Page 449• Problems 14-31