Chapter 9 Section 1 Exploring Circles

Vocabulary Circle- 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 = 2πr C = 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 = 2r 26 = 2r 13 = 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 = 2r 36 = 2r 18 = r

Example 3) The radius, diameter, or circumference of a circle is given Example 3) The radius, diameter, or circumference of a circle is given. Find the other measures to the nearest tenth. r = 5, d = ?, C = ? d = 2r d = 2(5) d = 10 d = 26.8, r = ?, C = ? 26.8 = 2r 13.4 = r C) C = 136.9, d = ?, r = ? C = 2πr 136.9 = 2πr 68.45 = πr 21.8 = r r = x/6, d = ?, C = ? d = 2r d = 2(x/6) d = x/3 d = 2x, r = ?, C = ? 2x = 2r x = r C = 2368, d = ?, r = ? C = 2πr 2368 = 2πr 1184 = πr 376.9 = r C = 2πr C = 2π(5) C = 10π C = 2πr C = 2π(x/3) C = (2xπ)/3 C = 2πr C = 2π(13.4) C = 26.8π C = 2πr C = 2π(x) C = 2πx d = 2r d = 2(21.8) d = 43.6 d = 2r d = 2(376.9) d = 753.8

Example 3) Refer to the figure to answer the questions. D A Example 3) Refer to the figure to answer the questions. Name the center of the circle. M Name a chord that is also a diameter. RI If MD = 5, find RI. d = 2r d = 2(5) d = 10 Is MI a chord of the circle? Explain. No, both the endpoints have to be on the circle for it to be a chord. R M I S U

Example 4) Refer to the figure to answer the questions. D A Example 4) Refer to the figure to answer the questions. Is MA congruent to MI? Explain. Yes; they are both radii of the circle and all the radii are congruent. Name four radii of the circle. RM, AM, DM, and IM If RI = 11.8, find MA. d = 2r 11.8 = 2r 5.9 = r Is RI > SU? Explain. Yes, RI is a diameter and the diameter is the longest chord. R M I S U

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 = dπ C = 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 8 cm M 5 cm M 12 cm So the diameter is 13 cm. C = dπ C = 13π