Circular segment

A circular segment, also called a disk segment, is the region of a disk that is cut off from the rest of the disk by a straight line. The line, taken in full, is a secant, and the part of it lying inside the disk is a chord. More formally the segment is the plane region bounded by a circular arc, by convention one of less than pi radians, and the chord joining its endpoints. It is described by the circle radius, the central angle, the chord length, the arc length, the sagitta or height, and the apothem, and its area equals the area of the circular sector minus the area of the triangle formed by the chord and the two radii, giving R squared over two times the angle minus its sine. The formulas are used in practical work such as finding the volume of liquid in a horizontal cylindrical tank, drawing round-topped doors and windows, and reconstructing a whole circular object from a fragment.