A circular sector is a wedge obtained by taking a portion of a disk with central angle radians (), illustrated above as the shaded region. A sector with central angle of radians would correspond to a filled semicircle. Let be the radius of the circle, the chord length, the arc length, the sagitta (height of the arced portion), and the apothem (height of the triangular portion). Then
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The angle obeys the relationships
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The area of the sector is
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(Beyer 1987). The area can also be found by direct integration as
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It follows that the weighted mean of the is
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so the geometric centroid of the circular sector is
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(Gearhart and Schulz 1990). Checking shows that this obeys the proper limits for a semicircle () and for an isosceles triangle ().