10-6 Circles & Arcs Lesson 10-6 GQ:

A CIRCLE is the set of all points equidistant from a given point called the center .; A B E AB AC radius diameter Circle B radius diameter

Types of Angles Central angle Inscribed angle - the vertex is on the center. Inscribed angle - the vertex is on the circle.

Types of Arcs Major arc Minor arc Semicircle P M O N or MN - the measure is more than 180 ° Example: MNO P - the measure is less than 180 ° Example: MO O - the measure is equal to 180 ° N or MN Example: MON

Measure of Arcs & Angles In a circle, the measure of the central angle is always equal to the measure of its intercepted arc. x = n m ∠ ABC = m AC n° C If ∠ ABC is 80°, what is the measure of arc AC? A x° B ° m AC = 80°

Measure of Arcs & Angles EXAMPLE: In the diagram below, if the m ∠ xyz is 68°, find the measure of a.) minor arc and b.) major arc. SOLUTION: a. measure of minor arc m ∠xyz = m xz (since ∠xyz is a central angle) x m xz = 68° b. measure of major arc major arc = 360° – m xz (minor arc) 68° =360° – 68° m xz (major arc) = 292° 68° y 292° z

The distance around a circle THM 10-9: Circumference The distance around a circle or

Find the circumference to the nearest tenth. 1. 2. 33 m 14.3 in. C = 89.8 in C = 103.7 m Exact answer: in terms of pi

a fraction of the circumference of a circle Arc Length a fraction of the circumference of a circle piece portion part section

THM 10-10: Arc Length THM the ratio of the length of an arc to the circumference is equal to the ratio of the measure of the arc to 360º

EX1: Find the length of arc AB to the nearest hundredth. 90º B 15 ft A  23.55 ft

Ex2: Find the measure of arc AB to the nearest degree. mAB = 120º

Ex3: Find the circumference of circle Q. A 41.87 cm Q 200º B C ≈ 75.37 cm