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Circle Properties

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Arc

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A contiguous segment of the circumference of a circle.

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Concentric Circles

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Circles that share the same center but have different radii.

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Sector

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The region of a circle bounded by two radii and the intercepted arc.

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Diameter

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A chord that passes through the center of the circle, calculated as d=2rd = 2r

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Pi (π)

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A mathematical constant, approximately equal to 3.14159, representing the ratio of a circle's circumference to its diameter.

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Circumference

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The perimeter of a circle, calculated with the formula C=2πrC = 2\pi r or C=πdC = \pi d

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Radius

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The distance from the center of the circle to any point on its circumference, represented by the letter r.

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Secant

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A line that intersects a circle at two points.

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Area

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The space enclosed by the perimeter of the circle, calculated with the formula A=πr2A = \pi r^2

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Chord

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A segment whose endpoints lie on the circle.

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Inscribed Angle

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An angle formed by two chords in a circle which share an endpoint.

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Tangent

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A line that intersects the circle at exactly one point.

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Central Angle

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An angle whose vertex is at the center of the circle and whose sides are radii.

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Cyclic Quadrilateral

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A quadrilateral where all four vertices lie on the circumference of a circle.

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Similar Circles

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Circles that have the same shape but differing sizes; their radii are proportional.

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Common Tangent

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A line or segment that is tangent to two circles.

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Tangent Circles

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Two circles that intersect at exactly one point.

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Chromatic Number of a Circle

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The minimum number of colors needed to color a plane such that no two points at distance exactly one from each other have the same color; for a circle, it equals 2.

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Annulus

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The region between two concentric circles of different radii.

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Circle Graph

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A graph where each vertex represents a chord of a circle, and two vertices are adjacent if and only if the chords intersect.

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