Circles Modified by Lisa Palen

Definitions Circle The CENTER of the circle is the point that is the same distance to every point on the circle. The distance from the center to the circle is called the RADIUS as well. The RADIUS is a segment from the center of the circle to a point on the circle. Symbol: The set of points in a plane at a given distance from a given point in that plane.

Definitions Chord A segment whose endpoints lie on the circle. Chord

Definitions Chord- A segment whose endpoints lie on the circle. A chord that contains the center of the circle. Diameter- Chord Diameter The DIAMETER of a circle is the length of any diameter as well.

Definitions Chord- A segment whose endpoints lie on the circle. A chord that contains the center of the circle. A line that contains a chord. Diameter- Secant- Chord Diameter Secant The DIAMETER of a circle is the length of any diameter as well.

EXAMPLE: Identify the chords, radii, and diameters. J

Tangent A line in the plane of the circle that intersects the circle in exactly one point. Point of Tangency Tangent The point where the tangent line intersects the circle. Definitions

CommonTangent A line in the plane of two or more circles that is tangent to each circle. Definitions

Congruent circles- circles that have congruent radii. 2 2 Concentric circles- circles that lie in the same plane and have the same center. Definitions

INSCRIBED POLYGON A polygon inside a circle whose vertices lie on the circle.

CIRCUMSCRIBED POLYGON A polygon whose sides are tangent to a circle.

ARC The part or portion on the circle from some point B to C is called an arc. A B C

ARCS Identify two different arcs.

ARC MEASURE Central angle – angle with vertex the center of a circle, with rays that intersect the circle The arc measure is the degree measure of the arc’s central angle. An arc’s central angle is the angle with vertex the center of the circle and rays passing through the arc’s endpoints. Central Angle

MINOR AND MAJOR ARCS A minor arc is an arc that measures less than 180° A major arc is an arc that measures more than 180°

SEMICIRCLE An arc that measures 180°.

ARCS Identify a minor arc, a major arc, and a semicircle, given that segment CD is a diameter.

NAMING ARCS A minor arc is named using its endpoints with an “arc” above. A major arc (or semicircle) is named using its endpoints along with another point on the arc (in order). or

NAMING ARCS How many different arcs can you name? NOTE: the chord EF is not a diameter.

ARC MEASURE NOTATION The arc measure is written: It is equal to the measure of the corresponding central angle. Central Angle

ADJACENT ARCS Two arcs of a circle that intersect at exactly one point. and are adjacent. A B C D

ARC ADDITION POSTULATE The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs. A B C D