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Circles
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Congruent Corresponding Chords Theorem
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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Perpendicular Chord Bisector Theorem & Converse
The diameter of a circle is perpendicular to a chord iff the diameter bisects the chord and its arc.
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What is the measure of Arc CD in the figure below?
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Equidistant Chords Theorem
In the same circle, or in congruent circles, two chords are congruent iff they are equidistant from the center.
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What is the value of x for the circle below?
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Intercepted Arc An inscribed angle is an angle whose vertex is on a circle. An Intercepted arc is the arc in the interior of the angle.
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Measure of an Inscribed Angle Theorem
The measure of an inscribed angle is half the measure of its intercepted arc.
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Inscribed Polygon A polygon is an inscribed polygon if all of its vertices lie on a circle. The circle that contains the vertices is circumscribed circle.
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Theorem A quadrilateral can be inscribed in a circle if and only if its opposite angles are supplementary.
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Practice P.553: 3-10, 15 P.562: 3-16
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