10.1 Tangent Line to Circle Theorem A line is tangent to a circle iff the line is perpendicular to a radius at the point of tangency. 10.2 External Tangent Congruence Theorem Tangent segments from the same external point are congruent. 10.3 Congruent Circles Theorem Two circles are congruent iff they have the same radius. 10.4 Congruent Central Angles Theorem In the same or congruent circles, two minor arcs are congruent iff their corresponding central angles are congruent. 10.5 Similar Circles Theorem All circles are similar. 10.6 Congruent Corresponding Chords Theorem In the same or congruent circles, two minor arcs are congruent iff their corresponding chords are congruent. 10.7 Perpendicular Chord Bisector Theorem If a diameter is perpendicular to a chord, then it bisects the chord and its arc. 10.8 Perpendicular Chord Bisector Converse If one chord is the perpendicular bisector of another chord, then the first chord is a diameter. 10.9 Equidistant Chords Theorem In the same or congruent circles, two chords are congruent iff they are equidistant from the center. 10.10 Measure of an Inscribed Angle Theorem The measure of an inscribed angle is half the measure of its intercepted arc. 10.11 Inscribed Angles of a Circle Theorem If two inscribed angles intercept the same arc, then the angles are congruent. 10.12 Inscribed Right Triangle Theorem If a right triangle is inscribed in a circle, then the hypotenuse is a diameter. Conversely, if one side of an inscribed triangle is a diameter, then the triangle is a right triangle. 10.13 Inscribed Quadrilateral Theorem A quadrilateral can be inscribed in a circle iff its opposite angles are supplementary. 10.14 Tangent and Intersected Chord Theorem If a tangent and chord intersect on a circle, then the angle formed equals half its intercepted arc. 10.15 Angles Inside the Circle Theorem If two chords intersect inside a circle, then the angle formed equals half the sum of the intercepted arcs. 10.16 Angles Outside the Circle Theorem If two secants, two tangents, or a tangent and secant intersect outside a circle, then the angle formed equals half the difference of the intercepted arcs. 10.17 Circumscribed Angle Theorem A circumscribed angle equals 180° minus the corresponding central angle. 10.18 Segments of Chords Theorem If two chords intersect inside a circle, then (part of chord 1)(other part of chord 1) = (part of chord 2)(other part of chord 2). 10.19 Segments of Secants Theorem If two secants share the same external endpoint, then (whole secant)(external part) = (whole secant)(external part). 10.20 Segments of Secants and Tangents Theorem If a secant and tangent share the same external endpoint, then (whole secant)(external part) = (tangent)^2.
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