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