10.6 Circles & Arcs

10.6 – Circles & Arcs Goals / “I can….” Find the measures of central angles and arcs Find circumference and arc length

10.6 – Circles & Arcs In a plane, a circle is the set of all points equidistant from a given point called the center. You name a circle by its CENTER C P A B

10.6 – Circles & Arcs Radius – a segment that has 1 endpoint at the center and the other on the circle Congruent circles have congruent radii Diameter – segment that contains the center and has both endpoints on the circle Central Angle – vertex is on the center C P A B

10.6 – Circles & Arcs Other 15% Sleep 31% Food 9% Work 20% Entertainment 18% Food 9% Must do 7% Work 20%

10.6 – Circles & Arcs An arc is part of a circle A semicircle is HALF of a circle ( = 180°) A minor arc is smaller than a semicircle ( < 180°) A major arc is larger than a circle ( > 180°)

10.6 – Circles & Arcs Identify the following in O Minor arcs Semicircle Major arcs that contain A A C B D O

10.6 – Circles & Arcs Find the measure of the following arcs: BC BD ABC AB 58° B D C O 32°

10.6 – Circles & Arcs Circumference of a circle: C = πd or C = 2πr d r

10.6 – Circles & Arcs A car has a turning radius of 16.1 ft. The distance between the 2 front tires is 4.7 ft. How much farther do the outside tires travel than the inside tires? 16 4.7

10.6 – Circles & Arcs Arc length AB = x 2πr mAB 360 r B O A

10.6 – Circles & Arcs Find the length of the arcs: 16 X Y O X Y O