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If a line is tangent to a circle,
then it is perpendicular to the radius drawn at the point of tangency
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
In the same circle or in congruent circles, two minor arcs are congruent
if and only if their corresponding arcs are congruent
If a diameter of a circle is perpendicular to a chord
then the diameter bisects the chord and its arc
In the same circle, or in congruent circles two chords are congurent
if and only if they are equidistant from the center
if a tangent and a chord intersect at a point on a circle
then the measure of each angle formed is one half the measure of the intercepted arc
If 2 chords intersect in the interior of a circle
then the measure of each angle is one half the measure of the 2 intercepted arcs
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