Geometry Section 10-1 1112

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Circles and Circumference

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Chapter 10:

Chapter 10 Circles

Section 10-1:

Section 10-1 Circles and Circumference

Essential Questions:

Essential Questions How do you identify and use parts of circles? How do you solve problems involving the circumference of a circle?

Vocabulary:

Vocabulary 1. Circle: The set of points that are all the same distance from a given point 2. Center: The point that all of the points of a circle are equidistant from 3. Radius: A segment with one endpoint at the center and the other on the edge of the circle; also the distance from the center to the edge of the circle 4. Chord: A segment with both endpoints on the edge of the circle

Vocabulary:

Vocabulary 5. Diameter: A special chord that passes through the center of a circle; twice the length of the radius 6. Congruent Circles: Two or more circles with congruent radii 7. Concentric Circles: Coplanar circles with the same center 8. Circumference: The distance around a circle 9. Pi (π): The irrational number found from the ratio of circumference to the diameter

Vocabulary:

Vocabulary 10. Inscribed: A polygon inside a circle where all of the vertices of the polygon are on the circle 11. Circumscribed: A circle that is around a polygon that is inscribed

Example 1:

Example 1 a. Name the circle Circle C or ⊙ C b. Identify a radius or c. Identify a chord d. Name the diameter

Example 2:

Example 2 If JT = 24 in, what is KM ? JT = KL KL = 24 in KM is half of KL KM = 12 in

Example 3:

Example 3 The diameter of ⊙ L is 22 cm and the diameter of ⊙P is 16 cm. MN = 5 cm. Find LP .

Example 4:

Example 4 Find the diameter and radius of a circle to the nearest hundredth if the circumference of the circle is 65.4 feet.

Example 5:

Example 5 Find the exact circumference of ⊙ R .

Check Your Understanding:

Check Your Understanding p. 687 #1-9

PRoblem Set:

PRoblem Set p. 685 #11-41 odd, 71 “We don't know who we are until we see what we can do.” - Martha Grimes

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