Geometry 10-1; 10-4

The circumference C of a circle with the diameter of d or a radius of r can be written in the form ____

C = (pi)d or C = 2(pi)r

diameters perpendicular to chords ____

bisect chords and intercepted arcs

central angle

center of the circle as its vertex, and its sides contain two radii of the circle

If two inscribed angels of a circle intercept congruent arcs or the same arc then the angles are____

congruent

the endpoints of a chord are also the ____

endpoints of an arc

the measure of the inscribed angle is ____

half the measure of its intercepted arc

In a circle, if a diameter (or radius) is perpendicular to a chord, then ____

it bisects the chord and its arc

If a quadrilateral is inscribed in a circle then ____

its opposite angels are supplementary

minor arc

part of a circle that measures less than 180

If an inscribed angle intercepts a semicircle ____

the angle is a right angle

The length of an arc is proportional to ____

the length of the circumference

circle

the locus of all points in a plane equidistant from a given point

The measure of each arc is related to ____

the measure of its central arc

360

the sum of the central angles of a circle with no interior points in common

Two arcs are congruent if and only if ____

their corresponding central angels are congruent

two minor arcs are congruent if and only if ____

their corresponding chords are congruent

two chords are congruent if and only if ____

they are equidistant from the center

For circles to be congruent circles ____

they must have congruent radii or congruent diameters

the diameter of a circle is ____

twice the radius

semicircle

an arc that measures 180

chord

any segment with endpoints that are on the circle

radius

any segment with endpoints that are the center and a point on the circle

To find angles of inscribed polygons, you can use ____

arc measures

arc length

(measure of the central angle/360) x (2 pi r)

major arc

an arc of a circle that is larger than a semicircle (more than 180°)

Arc Addition Postulate

The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs

Inscribed Angle Theorem

The measure of an inscribed angle of a circle is equal to 1/2 the measure of its intercepted arc

arc

a central angle separates the circle into two parts, each is this.

diameter

a chord that passes through the center

Inscribed

a circle (on the inside) of a polygon and only touches each side at exactly 1 point

Circumscribed

a circle (on the outside) that only passes through each vertex of a polygone