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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

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