2 A CIRCLE is the set of all points equidistant from a given point called the center .; A BEABACradiusdiameterCircle Bradiusdiameter
3 Types of Angles Central angle Inscribed angle - the vertex is on the center.Inscribed angle- the vertex is on the circle.
4 Types of Arcs Major arc Minor arc Semicircle P M O N or MN - the measure is more than 180 °Example: MNOP- the measure is less than 180 °Example: MOO- the measure is equal to 180 °Nor MNExample: MON
5 Measure of Arcs & Angles In a circle, the measure of the central angle is always equal to the measure of its intercepted arc.x = nm ∠ ABC = m ACn°CIf ∠ ABC is 80°, what is the measure of arc AC?Ax°B °m AC = 80°
6 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 arcm ∠xyz = m xz (since ∠xyz is a central angle)xm xz = 68°b. measure of major arcmajor arc = 360° – m xz (minor arc)68°=360° – 68°m xz (major arc) = 292°68°y292°z
7 The distance around a circle THM 10-9: CircumferenceThe distance around a circleor
8 Find the circumference to the nearest tenth. 1.2.33 m14.3 in.C = 89.8 inC = mExactanswer:in termsof pi
9 a fraction of the circumference of a circle Arc Lengtha fraction of the circumference of a circlepieceportionpartsection
10 THM 10-10: Arc Length THMthe ratio of the length of an arc to the circumference is equal to the ratio of the measure of the arc to 360º
11 EX1: Find the length of arc AB to the nearest hundredth. 90ºB15 ftA ft
12 Ex2: Find the measure of arc AB to the nearest degree. mAB = 120º
13 Ex3: Find the circumference of circle Q. A41.87 cmQ200ºBC ≈ cm
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