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33 Cards in this Set
- Front
- Back
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circle |
The set of all points in a plane that are at a given distance from a given point
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center of a circle |
The given point that is equidistant from all of the points on a circle. |
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concentric
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Circles are concentric iff they lie in the same plane and have the same center
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radius |
A radius of a circle is a line segment that connects the center of the circle to any point on it. The radius of a circle is the length of one of these line segments. |
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The plural of 'radius' is... |
radii. (Pronounced 'RAY-dee-eye') |
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Corollary to the definition of a circle. |
All radii of a circle are equal. |
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chord of a circle |
A chord of a circle is a line segment that connects two points of the circle.
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diameter |
A diameter of a circle is a chord that contains the center. The diameter of a circle is the length of one of these chords
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If a line through the center of a circle is perpendicular to a chord... |
then it also bisects the chord
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If a line through the center of a circle bisects a chord that is not a diameter, then...
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it is also perpendicular to the chord.
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The perpendicular bisector of a chord of a circle...
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contains the center of the circle.
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tangent
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A tangent to a circle is a line in the plane of the circle that intersects the circle in exactly one point.
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If a line is tangent to a circle...
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it is perpendicular to the radius drawn to the point of contact.
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If a line is perpendicular to a radius at its outer endpoint...
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it is tangent to the circle.
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A central angle of a circle
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is an angle whose vertex is the center of the circle.
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A reflex angle |
is an angle whose measure is more than 180°.
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The degree measure of an arc...
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is the measure of the arc’s central angle.
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The Arc Addition Postulate
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If point C is on arc AB, then the measure of arc AC + the measure of arc CB = the measure of arc ACB . |
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In a circle, equal chords have...
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equal arcs.
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In a circle, equal arcs have...
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equal chords.
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An inscribed angle is...
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an angle whose vertex is on a circle, with each of the angles sides intersecting the circle in another point. |
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An inscribed angle is equal in measure to...
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half its intercepted arc. |
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Inscribed angles that intercept the same arc...
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are equal. |
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An angle inscribed in a semicircle...
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is a right angle.
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A secant is a line that... |
intersects a circle in two points.
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A secant angle is an angle...
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whose sides are contained in two secants of a circle so that each side intersects the circle in at least one point other than the angle’s vertex. |
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The secant angle whose vertex is inside circle is equal in measure to...
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half the sum of the arcs intercepted by it and its vertical angle. |
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A secant angle whose vertex is outside a circle is equal in measure to...
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half the difference of its larger and smaller intercepted arcs. |
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Tangent segment to a circle
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If a line is tangent to a circle, then any segment of the line having the point of tangency as one of its endpoints is a tangent segment to the circle. |
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The tangent segments theorem. |
are equal.
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The Intersecting Chords Theorem |
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. |
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major arc
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An arc whose measure is greater than 180°.
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minor arc |
An arc whose measure is less than 180°. |
