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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

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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

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If 2 segments from the same exterior point are tangent to a circle

then they are congruent

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In the same circle or in congruent circles, two minor arcs are congruent

if and only if their corresponding arcs are congruent

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If a diameter of a circle is perpendicular to a chord

then the diameter bisects the chord and its arc

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A quadrilateral can be inscribed in a circle

if and only if its opposite angles are supplementary

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In the same circle, or in congruent circles two chords are congurent

if and only if they are equidistant from the center

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If an angle is inscribed in a circle

then its measure is half the measure of its intercepted arc

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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

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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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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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