the set of all points in a plane that are equidistant from a given poing, called the center of the circle.
common external tangent
a common tangent that does not intersect the segment that joins the centers of the circles.
common internal tangent
a common tangent that intersects the segment that joings the centers of the circles.
in a plane, a line is tangent to a cirlce if and only if the line is perpendicular to a radius of the circle at its endpoint on the circle.
if the measure of angle APB is less than 180 degrees, then the portion of the circle included between points A and B form this
this starts and ends with points A and B but it is the arc that lies in the exterior of angle APB.
arc addition postulate
the measure of an arc formed by two adjacent arcs is the sum of the measures of the 2 arcs
the arcs are congruent if they have the same measure and they are arcs of the same circle or of congruent circles.
in the same circle, or in congruent circles, 2 minor arcs are congruent if and only if their corresponding chords are congruent.
if one chord is a perpendicular bisector of another chord, then the first chord is a diameter.
if a diameter of a circle is perpendicular to a chord then the diameter bisects the chord and its arcs.
in the same circle, or in congruent circles, two chords are congruent if and only if they are equidistant from the center.
the arc that lies in the interior of an inscribed angle and has endpoints on the angle.