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
If 2 segments from the same exterior point are tangent to a circle
then they are congruent
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
A quadrilateral can be inscribed in a circle
if and only if its opposite angles are supplementary
In the same circle, or in congruent circles two chords are congurent
if and only if they are equidistant from the center
If an angle is inscribed in a circle
then its measure is half the measure of its intercepted arc
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
If a tangent and a secant, two tangents or two secants intersect in the exterior of circle
then the measure of the angle formed is one half the difference of the intercepted arc
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