 | Term | Definition |
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a set of points in a plane at a given distance from a given point in that plane |
Circle |
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the given point of the circle |
Center |
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the given distance |
Radius |
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segment whose endpoints lie on a circle |
Chord |
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a line that contains a chord |
Secant |
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a chord that contains the center of a circle |
Diameter |
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line in the plane of a circle that intersects the circle in exactly one point |
Tangent |
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set of all points in a space at a distance |
Sphere |
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circles that have congruent radii |
Congruent circles |
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spheres that have congruent radii |
Congruent spheres |
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circles that lie in the same plane and have the same center |
Concentric circles |
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sphere that have the same center |
Concentric spheres |
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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 |
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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Tangents to a circle from a point are congruent |
Tangents to a circle from a point are congruent |
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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 |
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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A line that is tangent to each of two coplanar circles |
Common tangent |
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angle with its vertex at the center of a circle |
Central angle |
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The measure of the arc formed by two adjacent arcs is the sum of the measures of these two arcs |
Arc Addition Postulate |
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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 |
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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In the same circle or in congruent circles: congruent arcs have congruent chords |
In the same circle or in congruent circles: congruent arcs have congruent chords |
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In the same circle or in congruent circles: Congruent chords have congruent arcs |
In the same circle or in congruent circles: Congruent chords have congruent arcs |
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A diameter that is perpendicular to a chord bisects the chord and its arc |
A diameter that is perpendicular to a chord bisects the chord and its arc |
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In the same circle or in congruent circles: Chords equally distant from the center are congruent |
In the same circle or in congruent circles: Chords equally distant from the center are congruent |
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In the same circle or in congruent circles: Congruent chords are equally distant from the center |
In the same circle or in congruent circles: Congruent chords are equally distant from the center |
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an angle whose vertex is on a circle and whose sides contain chords of the circle |
Inscribed angle |
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The measure of an inscribed angle is equal to half the measure of its intercepted arc |
The measure of an inscribed angle is equal to half the measure of its intercepted arc |
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If two inscribed angles intercept the same arc, then the angles are congruent |
If two inscribed angles intercept the same arc, then the angles are congruent |
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An angle inscribed in a semicircle is a right angle |
An angle inscribed in a semicircle is a right angle |
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If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary |
If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary |
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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 |
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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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 |
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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The measure of an angle formed by two secants, two tangents, or a secant and a tangent drawn from a point outside the circle is equal to half the difference of the measures of the intercepted arcs |
The measure of an angle formed by two secants, two tangents, or a secant and a tangent drawn from a point outside the circle is equal to half the difference of the measures of the intercepted arcs |
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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 |
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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When two secant segments are drawn to a circle from an external point, the product of one secant segment and its external segment equals the product of the other secant segment and its external segment |
When two secant segments are drawn to a circle from an external point, the product of one secant segment and its external segment equals the product of the other secant segment and its external segment |
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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 |
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 |
