Circles and ArcsCircles and Arcs

Objectives:Objectives:

To find the measures of To find the measures of central angles and arcscentral angles and arcs

To find the circumference and To find the circumference and arc lengtharc length

• Circle– The set of all points in a plane at a

given distance (radius) from a given point (center) in the plane.

– Name a circle by its center point.

• Radius– A segment from the center to a point

on the edge of the circle.

• Diameter– A line segment containing the center,

with its endpoints on the circle.

• Congruent Circles– Two or more circles with the same

radius.

• Concentric Circles - Two or more coplanar circles with the

same center

P

• Circumference of a Circle

• π (pi) times the diameter

• Arc of a circle– Two points on the circle and the continuous

(unbroken) part of the circle between the two points (endpoints).

• Semicircle– An arc of a circle whose endpoints are the

endpoints of a diameter.– Notation: Three points name arc (endpoints

with any other point on arc in middle)• Minor arc

– An arc of a circle that is smaller than a semicircle.

– Notation: Two endpoints name arc.• Major arc

– An arc of a circle that is larger than a semicircle– Notation: Same as semicircle

• Arc measure– Central angle: angle with its vertex at the center

of the circle and the sides passing through endpoints of the arc.

A B

Notation: AB

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