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34 Cards in this Set
- Front
- Back
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circle
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set of points in a plane at a given distance from a given point in that plane
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congruent circles
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are circles that have congruent radii
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concentric circles
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circles that lie in the same plane and have the same center
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concentric spheres
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spheres that have the same center
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theorem 9-1
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if a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency
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corollary
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tangents to a circle from a point are congruent
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theorem 9-2
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if a line in the plane of a circle is perpendicular to a radius at its outer endpoint then the line is tangent to the circle.
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common tangent
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a line that is tangent to each of two coplanar circles
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tangent circles
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coplanar circles that are tangent to the same line at the same point
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central angle
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angle with its vertex at the center of the circle
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semicircles
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the endpoints of a diameter
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measure of a minor arc
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measure of central angle
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measure of a major arc
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360 minus the measure of the minor arc
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adjacent arcs
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arcs that have exactly one point in common
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Arc Addition Postulate
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the measure of the arc formed by two adjacent arcs is the sum of the measures of these two arcs
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congruent arcs
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arcs in the same circle or in congruent circles that have equal measures
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Theorem 9-3
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in the same circle or in congruent circles, two minor arcs are congruent if and only if their central angles are congruent
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Theorem 9-4
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In the same circles:
1) Congruent arcs have congruent chords. 2) Congruent chords have congruent arcs. |
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Theorem 9-5
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A diameter that is perpendicular to a chord bisects the chord and its arc.
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Theorem 9-6
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In the same circle or in congruent circles:
1) Chords equally distant from the center (or centers) are congruent. 2) Congruent chords are equally distant from the center (or centers). |
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inscribed angle
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angle whose vortex is on a circle and whose sides contain chords of the circle
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Theorem 9-7
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The measure of an inscribed angle is equal to half the measure of its intercepted arc.
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Corollary 1
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If two inscribed angles intercept the same arc, then the angles are congruent.
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Corollary 2
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An angle inscribed in a semicircle is a right angle.
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Corollary 3
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If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary.
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Theorem 9-8
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The measure of an angle formed by a chord and a tangent is equal to half the measure of the intercepted arc.
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Theorem 9-9
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The measure of an angle formed by two chords that intersect inside a circle is equal to half the sum of the measures of the intercepted arcs.
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Theorem 9-10
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The measure of an angle formed by two secants, two tangents, or a secant and a tangent drawn from a point outside a circle is equal to half the difference of the measures of the intercepted arcs.
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Theorem 9-11
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When two chords intersect inside a circle, the product of the segments of one chord equals the product of the segments of the other chord.
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Theorem 9-12
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When two secant segments are drawn to a circle from an external segment equals the product of the other secant segment and its external segment.
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Theorem 9-13
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When a secant segment and a tangent segment are drawn to a circle from an external point, the product of the secant segment and its external segment is equal to the square of the tangent segment.
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True or False
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Tangents to a circle from a point are congruent.
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True or False
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If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency.
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True or False
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The converse of:
If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency. |
