10.1 Circles and Circumference. Objectives Identify and use parts of circles Identify and use parts of circles Solve problems using the circumference.

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Presentation transcript:

10.1 Circles and Circumference

Objectives Identify and use parts of circles Identify and use parts of circles Solve problems using the circumference of circles Solve problems using the circumference of circles

Parts of Circles Circle – set of all points in a plane that are equidistant from a given point called the center of the circle. Circle – set of all points in a plane that are equidistant from a given point called the center of the circle. A circle with center P is called “circle P” or P. A circle with center P is called “circle P” or P. P

Parts of Circles The distance from the center to a point on the circle is called the radius of the circle. The distance from the center to a point on the circle is called the radius of the circle. The distance across the circle through its center is the diameter of the circle. The diameter is twice the radius d = 2r or r = ½ d). The distance across the circle through its center is the diameter of the circle. The diameter is twice the radius d = 2r or r = ½ d). The terms radius and diameter describe segments as well as measures. The terms radius and diameter describe segments as well as measures.

Parts of Circles QP, QS, and QR are radii. QP, QS, and QR are radii. All radii for the same circle are congruent. All radii for the same circle are congruent. PR is a diameter. PR is a diameter. All diameters for the same circle are congruent. All diameters for the same circle are congruent. A chord is a segment whose endpoints are points on the circle. PS and PR are chords. A chord is a segment whose endpoints are points on the circle. PS and PR are chords. A diameter is a chord that passes through the center of the circle. A diameter is a chord that passes through the center of the circle.

Name the circle. Answer: The circle has its center at E, so it is named circle E, or. Example 1a:

Answer: Four radii are shown:. Name the radius of the circle. Example 1b:

Answer: Four chords are shown:. Name a chord of the circle. Example 1c:

Name a diameter of the circle. Answer: are the only chords that go through the center. So, are diameters. Example 1d:

Answer: a. Name the circle. b. Name a radius of the circle. c. Name a chord of the circle. d. Name a diameter of the circle. Answer: Your Turn:

Answer: 9 Formula for radius Substitute and simplify. If ST 18, find RS. Circle R has diameters and. Example 2a:

Answer: 48 Formula for diameter Substitute and simplify. If RM 24, find QM. Circle R has diameters. Example 2b:

Answer: So, RP = 2. Since all radii are congruent, RN = RP. If RN 2, find RP. Circle R has diameters. Example 2c:

Answer: 58 Answer: 12.5 a. If BG = 25, find MG. b. If DM = 29, find DN. Circle M has diameters c. If MF = 8.5, find MG. Answer: 8.5 Your Turn:

Find EZ. The diameters of and are 22 millimeters, 16 millimeters, and 10 millimeters, respectively. Example 3a:

Since the diameter of FZ = 5. Since the diameter of, EF = 22. Segment Addition Postulate Substitution is part of. Simplify. Answer: 27 mm Example 3a:

Find XF. The diameters of and are 22 millimeters, 16 millimeters, and 10 millimeters, respectively. Example 3b:

Since the diameter of, EF = 22. Answer: 11 mm is part of. Since is a radius of Example 3b:

The diameters of, and are 5 inches, 9 inches, and 18 inches respectively. a. Find AC. b. Find EB. Answer: 6.5 in. Answer: 13.5 in. Your Turn:

Circumference The circumference of a circle is the distance around the circle. In a circle, The circumference of a circle is the distance around the circle. In a circle, C = 2r or d

Find C if r = 13 inches. Circumference formula Substitution Answer: Example 4a:

Find C if d = 6 millimeters. Circumference formula Substitution Answer: Example 4b:

Find d and r to the nearest hundredth if C = 65.4 feet. Circumference formula Substitution Use a calculator. Divide each side by. Example 4c:

Radius formula Use a calculator. Answer: Example 4c:

a. Find C if r = 22 centimeters. b. Find C if d = 3 feet. c. Find d and r to the nearest hundredth if C = 16.8 meters. Answer: Your Turn:

Read the Test Item You are given a figure that involves a right triangle and a circle. You are asked to find the exact circumference of the circle. MULTIPLE- CHOICE TEST ITEM Find the exact circumference of. A B C D Example 5:

Solve the Test Item The radius of the circle is the same length as either leg of the triangle. The legs of the triangle have equal length. Call the length x. Pythagorean Theorem Substitution Divide each side by 2. Simplify. Take the square root of each side. Example 5:

So the radius of the circle is 3. Circumference formula Substitution Because we want the exact circumference, the answer is B. Answer: B Example 5:

Answer: C Find the exact circumference of. A B C D Your Turn:

Assignment Geometry Pg. 526 #16 – 42 all, 44 – 54 evens Geometry Pg. 526 #16 – 42 all, 44 – 54 evens Pre-AP Geometry Pg. 526 # Pre-AP Geometry Pg. 526 #