Warm Up Make a list of activities you take part in each day. Give each activity a percentage value which represents the amount of time you spend doing that activity. (%s should add to 100) Example: Sleep – 29% Must Do – 8% Work - 46% Food – 4% Entertainment – 13%

Section 7 –6 Circles & arcs Objectives: To find the measures of central angles and arcs To find circumference and arc length

Circles – The set of all points equidistant from the center. Central Angle: An angle whose vertex is the center of a circle.

Example 1 Real-World Connection A) Use the circle graph from the warm up to find the measure of each central angle.

B) A researcher surveyed 2000 members of a golf club to find their ages. The graph shows the survey results. Find the measure of each central angle in the circle graph.

Arcs of a Circle SEMICIRCLE – Minor Arc – Major Arc – Half of a circle Smaller than a semicircle Major Arc – Larger than a semicircle

Example 2 Identifying Arcs Identify the following in circle O. The minor arcs The major arcs that contain point A The semicircles

D) Name the four major arcs that contain point E.

Adjacent Arcs: Arcs of the same circle that have exactly one point in common. Arc Addition Postulate The measure of the arc formed by two adjacent arcs is the sum of the measures of the two arcs.

Example 3 Finding the Measures of Arcs Find the measure of each arc. A) Arc BC Arc BD Arc ABC Arc AB

Find the measure of each arc. Arc MW Arc XW Arc YMW Arc MXD Arc MXW

Homework Textbook Page 389- 390; #1 – 26 All

Objectives: To find circumference and arc length Section 7 –6 Continued… Objectives: To find circumference and arc length

Circumference– 𝐶=2𝜋𝑟 𝐶=𝜋𝑑

Example 4 Real-World Connection A) A car has a turning radius of 16.1 feet. The distance between the two front tires is 4.7 feet. In completing the outer turning circle, how much farther does a tire travel than a tire on the concentric inner circle.

B). A circular swimming pool with a 16 ft B) A circular swimming pool with a 16 ft. diameter will be enclosed in a circular fence 4 feet from the pool. What length of fencing material is needed? Round to the nearest whole number.

C). The diameter of a bicycle wheel is 22 in C) The diameter of a bicycle wheel is 22 in. To the nearest whole number, how many revolutions does the wheel make when the bicycle travels 100 feet?

Arc Length: Theorem 7 – 14: Arc Length A fraction of a circle’s circumference Theorem 7 – 14: Arc Length The length of an arc of a circle is the product of the ratio 𝒎𝒆𝒂𝒔𝒖𝒓𝒆 𝒐𝒇 𝒕𝒉𝒆 𝒂𝒓𝒄 𝟑𝟔𝟎 and the circumference of the circle.

Example 5 Finding Arc Length Find the length of each arc shown. Leave your answer in terms of π.

C) Find the length of arc ADB in Circle M in terms of π. D) Find the length of a semicircle with radius 1.3 m. Leave your answer in terms of π.

Congruent Arcs: Arcs that have the same measure and are in the same circle or are in congruent circles.

Homework Textbook Page 390- 391; #27-39 Odd, 42 – 52 Even