Chapter 11Circles

Section 11-1Parts of a Circle

CircleA circle is the set of all points in a plane that are a given distance from a given point in the plane, called the center of the circle.

Segments of a CirlceRadius – has one endpoint on the center and one on the circle

Chord – has both endpoint on the circle

Diameter – a chord that passes through the center

Theorem 11-1All radii of a circle are congruent.

Theorem 11-2The measure of the diameter of a circle is twice the measure of the radius of the circle.

Section 11-2Arcs and Central

Angles

Types of ArcsMinor Arc – measure is less than 180°

Major Arc – measure is greater than 180°

Semicircle – measure equals 180°

Definition of Arc MeasureThe degree measure of a minor arc is the degree measure of its central angle.

The degree measure of a major arc is 360 minus the degree measure of its central angle.

The degree measure of a semicircle is 180.

Postulate 11-1The sum of the measures of two adjacent arcs is the measure of the arc formed by the adjacent arcs.

Theorem 11-3In a circle or in congruent circles, two minor arcs are congruent if and only if their corresponding central angles are congruent.

Section 11-3Arcs and Chords

Theorem 11-4In a circle or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent.

Theorem 11-5In a circle, a diameter bisects a chord and its arc if and only if it is perpendicular to the chord.

Section 11-4Inscribed Polygons

Inscribed PolygonA polygon is inscribed in a circle if and only if every vertex of the polygon lies on the circle.

The circle is circumscribed about the polygon

Theorem 11-6In a circle or in congruent circles, two chords are congruent if and only if they are equidistant from the center.

Section 11-5Circumference of a

Circle

CircumferenceThe distance around a circle

Theorem 11-7If a circle has a circumference of C units and a radius of r units, then C= 2r or C = d.

Section 11-6Area of a Circle

Theorem 11-8If a circle has an area of A square units and a radius of r units, then A = r2

Theorem 11-9If a sector of a circle has an area of A square units, a central angle measurement of N degrees, and a radius of r units, then A = N/360(r2)