set of all points in a plane that are equidistant from a given point
the point that all points on a circle are equidistant to
a segment whose endpoints are the center and any point on the circle
a segment whose endpoints are on a circle
a chord that contains the center of the circle
a line that intersects a circle in two points
a line, segment, or ray in the plane of a circle that intersects the circle in exactly one point
point of tangency
the one point where the tangent intersects the circle
coplanar circles that intersect in one point
coplanar circles that have a common center
a line, ray, or segment that is tangent to two coplanar circles
Perpendicular Radius to a Tangent Theorem
In a plane, a line is tangent to a circle if and only if the line is perpendicular to a radius of the circle at its endpoint on the circle.
Congruent Tangents to External Point Theorem
Tangent segments from a common external points are congruent.
an angle whose vertex is the center of the circle
an arc of a circle whose measure is less than 180 degrees
an arc of a circle whose measure is more than 180 degrees
an arc with endpoints that are the endpoints of a diameter
measure of a minor arc
measure of its central angle
measure of a major arc
360-measure of related minor arc
measure of a semicircle
arc addition postulate
The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs.
circles with the same radius
arcs with the same measure that are part of the same circle or of congruent circles
Congruent Corresponding Chords and Minor Arcs Theorem
In the same circle, or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent.
Perpendicular Bisecting Chords & Arcs Theorem
If one chord is a perpendicular bisector of another chord, then the first chord is a diameter.
Perpendicular Bisecting Chords & Arcs Converse
If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc.
Equidistant Congruent Chords from the Center Theorem
In the same circle, or in congruent circles, two chords are congruent if and only if they are equidistant from the center.
an angle whose vertex is on a circle and whose sides contain chords of the circle
the arc that lies in the interior of an inscribed angle and has endpoints on the angle
Measure of an Inscribed Angle Theorem
The measure of an inscribed angle is one half the measure of its intercepted arc.
Congruent Inscribed Angles with the Same Arc Theorem
If two inscribed angles of a circle intercept the same arc, then the angles are congruent.
Hypotenuse of an Inscribed Right Triangle is a Diameter Theorem
If a right triangle is inscribed in a circle, then the hypotenuse is a diameter of the circle.
Hypotenuse of an Inscribed Right Triangle is a Diameter Converse
If one side of an inscribed triangle is a diameter of the circle, then the triangle is a right triangle and the angle opposite the diameter is the right angle.
Supplementary Opposite Angles in an Inscribed Quadrilateral Theorem
A quadrilateral can be inscribed in a circle if and only if its opposite angles are supplementary.
segments of a chord
when two chords intercept in the interior of a circle, each chord is divided into two segments that are called...
Segments of a Chord Theorem
If two chords intersect in the interior of a circle, then the product of the lengths of the segments of one chord is equal to the products of the lengths of the segments of the other chord.
Segments of Secants Theorem
If two secant segments share the same endpoint outside a circle, then the product of the lengths of one secant segment and one external segment equals the product of the lengths of the other secant segment and its external segment.
Segments of Secants and Tangents Theorem
If a secant segment and a tangent segment share an endpoint outside a circle, then the product of the lengths of the secant segment and its external segments equals the square of the length of the tangent segment.
standard equation of a circle
(x-h)² + (y-k)² = r²
simple equation of a circle
x² + y² = r²