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also see Defining Geometric Figures

 Circle All points on the circumference of a circle are equidistant from its center. Radius: r Diameter: d Circumference: C Area: K d = 2r C = 2 Pi r = Pi d   K = Pi r2 = Pi d2/4 C = 2 sqrt(Pi K)   K = C2/4 Pi = Cr/2 To read about circles, visit The Geometry Center.

 Arc of a Circle A curved portion of a circle. Length: s   Central angle:      theta (in radians),      alpha (in degrees)       s = r theta = r alpha Pi/180

 Segment of a Circle Either of the two regions into which a secant or a chord cuts a circle. (However, the formulas below assume that the segment is no larger than a semi-circle.) Chord length: c Height: h Distance from center of circle to chord's midpoint: d Central angle: theta (in radians), alpha (in degrees)   Area: K Arc length: s theta = 2 arccos(d/r) = 2 arctan(c/(2d)) = 2 arcsin(c/(2r))      h = r - d      c = 2 sqrt(r2-d2) = 2r sin(theta/2) = 2d tan(theta/2) = 2 sqrt[h(2r-h)]      d = sqrt(4r2-c2)/2 = r cos(theta/2) = c cot(theta/2)/2      K = r2[theta-sin(theta)]/2 = r2arccos([r-h]/r) - (r-h)sqrt(2rh-h2)          = r2arccos(d/r) - d sqrt(r2-d2)      theta = s/r      K = r2[s/r - sin(s/r)]/2 For much more about segments of circles, see The Arc, Chord, Radius, Height, Angle, Apothem, and Area.

 Sector of a Circle The pie-shaped piece of a circle 'cut out' by two radii. Central angle:      theta (in radians),      alpha (in degrees)   Area: K Arc length: s      K = r2theta/2 = r2alpha Pi/360      theta = s/r      K = rs/2

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