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Theorems and definitions

Circle set of all points in a place that are equidistant from a given point called the center of the circle
Chord a segment whose endpoints are points on the circle (inside)
Secant a line that intersects a circle in two points (outside)
Tangent a line that intersects a circle in exactly one point
concentric coplanar circles that have a common center
common tangent a line or segment that is tangent to two coplanar circles
point of tangency the point at which a tangent line intersects the circle to which it is tangent
Theorem 1 if a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency
Theorem 2 in a plane, if a line is perpendicular to a radius of a circle at its endpoint on the circle, then the line is tangent to the circle
theorem 3 if two segments from the same exterior point are tangent to a circle, then they are congruent
central angle an angle whose vertex is the center of the circle
minor arc part of a circle that measures less that 180; named with two letters
Major Arc part of a circle that measures between 180 and 360; named with three letters
Semicircle an arc whose endpoints are the endpoints of a diameter of the circle
Measure of a Minor Arc the measure of its central angle
Measure of a Major Arc the difference between 360 and the measure of its associated minor arc
Congruent Arc two arcs of the same circle or of congruent circles that have the same measures
Arc Addition Postulate the measure of an arc formed by two adjacent arcs is the sum of the measure of the two arcs
Theorem 4 in the same circle, or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent
Theorem 5 If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc
Theorem 6 If one chord is a perpendicular bisector of another chord, then the first chord is a diameter
Theorem 7 In the same circle, or in congruent circles, two chords are congruent if and only if they are equidistant from the center
Created by: McChicklet