Chapter 10 Thorems/ Collaries/ Postulates
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| Arc Addition Postulate | the measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs
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| in a plane, a line is tangent to a circle if and only if the line is perpendicular to a radius of the circle at its endpoint on the circle
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| tangent segments from a common external point 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 chords are congruent
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| if one chord is a perpendicular bisector of another chord, then the first chord is a diameter
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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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| in the same circle, or in congruent circles, two chords are congruent if and only if they are equidistant from the center
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| Measure of an Inscribed Angle Theorem | the measure of an inscribed angle is one half the measure of its intercepted arc
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| if two inscribed angles of a circle intercept the same arc, then the angles are congruent
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| if a right triangle is inscribed in a circle, then the hypotenuse is a diameter of the circle. Conversely, if one side of an inscribed triangle is a diameter of the circle, then the triangle is a right triangle and the angle opposite the diameter is the
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| right angle
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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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| 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 its intercepted arc
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| Angles Inside the Circle | if two chords intersect inside a circle, then the measure of each angle is one half the sum of the measures of the arcs intercepted by the angle and its vertical angle
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| Angles Outside the Circle | If a tangent and a secant, two tangents, or two secants intersect outside a circle, then the measure of the angle formed is one half the difference of the measures of the intercepted arcs
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| Segments of Chords Theorem | if two chords intersect in the interior of a circle, then the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord
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| Segments of Secants Theorem | if two secant segments share the same endpoint outside a circle, then the product of the lengths of one secant segment and its external segment equals the product of the lengths of the other secant segment and its external segment
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| Segments of Secants and Tangents Theorem | if a secant segment and a tangent segment share an endpoint outside the circle, then the product of the lengths of the secant segment and its external segment equals the square of the length of the tangent segment
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