## Circular Sections

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

- Radius r
- Arc b
- Chord s
- Distance d
- Arrow height h
- Area of the circular section A1
- Angle at the center α

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