## 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.