## 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