Geometry 2D

Circular Sections

Given two of the following elements of a circular section the other ones are calculated.

In addition, the area of the circular segment, the circular area and the circumference will be calculated.

Example:

Given:
¯¯¯¯¯¯ 
                 Arc b = 1
             Angle α = 45°

Results:  
¯¯¯¯¯¯¯ 
           Radius r = 1,2732395
            Chord s = 0,97449536
       Section A1 = 0,63661977
       Distance d = 1,17632
 Arrow height h = 0,096919589
    Segment A2 = 0,063460604

             Area A = 5,0929582
     Perimeter p = 8

Application:

From a fragment of a plate the size of the original plate is to be calculated, when a chord s and the corresponding arrow height h can be measured.

Given:
¯¯¯¯¯¯  
            Chord s = 21
 Arrow height h = 6

Results:  
¯¯¯¯¯¯¯
           Radius r = 12,1875
            Angle α = 118,97953°
                Arc b = 25,308373
       Section A1 = 154,2229
       Distance d = 6,1875
    Segment A2 = 89,254148

             Area A = 466,63696
     Perimeter p = 76,576321

Result: The original plate had a radius of 12.2 cm.

See also:

Adjusting the Coordinate System
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