Studied by 0 peoplecircle
the set of all points in a plane a given distance from a given point in that plane called the center
radius
distance from the center to the circle
chord
a segment whose endpoints lie on the circle
diameter
a chord that intersects the center of a circle
tangent
a line in the plane of a circle that intersects the circle in exactly one point
point of tangency
the point where a tangent intersects the circle
secant
a line that contains a chord
sphere
the set of all points in space a given distance from a given point called the center
congruent circles
circles that have congruent radii
concentric circles
circles that lie in the same plane and have the same center
if a line is tangent to a circle,
then the line is perpendicular to the radius drawn to the point of tangency
tangents to a circle from the same point are
congruent
if a line in the plane of a circle is perpendicular to a radius at its outer endpoint,
then the line is tangent to the circle
when each side of a polygon is tangent to a circle,
the circle is inscribed in the polygon
common tangents
a line that is tangent to each of the two coplanar circles
common INTERNAL tangent
intersects the segment joining the centers
common EXTERNAL tangent
does NOT intersect the segment joining the centers
tangent circles
coplanar circles that are tangent to the same line at the same point
INTERNALLY tangent CIRCLES
circles that share interior points
EXTERNALLY tangent CIRCLES
circles that share NO common interior points
central angle
angle with its vertex at the center of a circle
arc
unbroken part of a circle
minor arc
arc of a circle that measures 0<x<180
major arc
arc of a circle that measures 180<x<360
semicircle
arc of a circle that measures 180
minor arc measure
equal to the measure of the central angle
major arc measure
360 - measure of its minor arc
semicircle measure
180
adjacent arcs
2 arcs in the same circle that share exactly one point
arc addition postulate
the measure of the arc formed by adjacent arcs is the sum of the measures of these 2 arcs
congruent arcs
arcs in the same circle or congruent circles that have the same measure
in the same circle or congruent circles, 2 minor arcs are
congruent iff their central angles are congruent
in the same circle or in congruent circles,
congruent arcs have congruent chords
congruent chords have congruent arcs
a diameter (or radius) that is perpendicular to a chord bisects
both the chord and its arc
in the same circle or congruent circles,
chords equidistant from the center (or centers) are congruent
congruent chords are equidistant from the center (or centers)
inscribed angle
an angle whose vertex is on a circle and whose sides contain chords of the circle
the measure of an inscribed angle is equal to
HALF the measure of its intercepted arc
if 2 inscribed angles intercept the same arc,
then the angles are congruent
an angle inscribed in a semicircle is
a right angle
if a quadrilateral is inscribed in a circle,
then its opposite angles are supplementary
the measure of an angle formed by a chord and a tangent is equal to
HALF the measure of the intercepted arc
the measure of an angle formed by 2 chords that intersect INSIDE a circle is equal
to half times the SUM of the measures of the intercepted arcs
the measure of an angle formed by 2 secants, 2 tangents, or a secant and a tangent drawn from a point OUTSIDE a circle is equal
to half times the difference of the measures of the intercepted arcs
when 2 chords intersect inside a circle, the PRODUCT of the segments of one chord equals
the PRODUCT of the segment of the other chord
when 2 secant segments are drawn to a circle from an external point, the product of one secant segment and its external segment equals
the product of the other segments and its external segments
when a segment segment and a tangent segment are drawn to a circle from an external point, the product segment is equal
to the square of the tangent segment
Note
Flashcard