CHAPTER 9SECTION 1

Exploring Circles

VOCABULARYCircle- The set of all points in a plane that are a given distances from a given point in that plane. Center- The given point is the center of the circle. Radius- A segment that has one endpoint at the center of the circle and the other endpoint in the circle. Chords- A segment that has its endpoints on the circle. Diameter- A chord that contains the center of the circle. 

r

VOCABULARY CONT.Circumference- The distance around the circle. Π(pi)- The ratio of the circumference of a circle to its diameter. Circumference of a Circle- C = 2πrC = dπ

Example 1) The size of a bicycle is determined by the diameter of the wheel. So, a 26-inch bicycle has a wheel with a 26-inch diameter. What is the length of a spoke of a 26-inch bicycle?The spoke is half the length of the diameter so the spoke would be the length of the radius.

d = 2r26 = 2r13 = r

Example 2) The size of a bicycle is determined by the diameter of the wheel. So, a 36-inch bicycle has a wheel with a 36-inch diameter. What is the length of a spoke of a 36-inch bicycle?The spoke is half the length of the diameter so the spoke would be the length of the radius.

d = 2r36 = 2r18 = r

Example 3) The radius, diameter, or circumference of a circle is given. Find the other measures to the nearest tenth.A) r = 5, d = ?, C = ?d = 2rd = 2(5)d = 10

B) d = 26.8, r = ?, C = ?

d = 2r26.8 = 2r13.4 = r

C) C = 136.9, d = ?, r = ?

C = 2πr136.9 = 2πr68.45 = πr21.8 = r

C = 2πrC = 2π(5)C = 10π

C = 2πrC =

2π(13.4)

C = 26.8πd = 2rd = 2(21.8)d = 43.6

D) r = x/6, d = ?, C = ?

d = 2rd = 2(x/6)d = x/3

E) d = 2x, r = ?, C = ?

d = 2r2x = 2rx = r

F) C = 2368, d = ?, r = ?

C = 2πr2368 = 2πr1184 = πr376.9 = r

C = 2πrC = 2π(x/3)C = (2xπ)/3

C = 2πrC = 2π(x)C = 2πx

d = 2rd =

2(376.9)

d = 753.8

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Example 3) Refer to the figure to answer the questions.

A) Name the center of the circle.M

B) Name a chord that is also a diameter.RI

C) If MD = 5, find RI.d = 2rd = 2(5)d = 10

D) Is MI a chord of the circle? Explain.No, both the endpoints have to be on the circle for it to be a chord.

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Example 4) Refer to the figure to answer the questions.

A) Is MA congruent to MI? Explain.Yes; they are both radii of the circle and all the radii are congruent.

B) Name four radii of the circle.RM, AM, DM, and IM

C) If RI = 11.8, find MA.d = 2r11.8 = 2r5.9 = r

D) Is RI > SU? Explain.Yes, RI is a diameter and the diameter is the longest chord.

M8 cm

Example 5) Find the exact circumference of the circle.

Since the side of the square is 8 cm, the diameter of the circle is also 8 cm.

C = dπC = 8π

Example 6) Find the exact circumference of the circle.

Since we have a right triangle we can find the diameter using the Pythagorean Theorem.

a2 + b2 = c2

52 + 122 = c2

25 + 144 = c2

169 = c2

13 = c

5 cm

12 cm

M

So the diameter is 13 cm.C = dπC = 13π