2. Geometry
a. Nomenclature; Geometric elements
Δ: Central angle; also the deflection angle between the tangents. R: Radius L: Arc length C: Chord length T: Tangebt distance 

Figure F1 Parts and Nomenclature 
Equation F1  Equation F2  Equation F3 
When dealing with highway or railroad alignments, another geometric element is often specified: degree of curvature, D. There are two different degree of curvature definitions:
D_{A}, arc definition; the angle subtended by a 100.00' arc, Figure F2(a).
D_{C}, chord definition; the angle subtended by a 100.00' chord, Figure F2(b).
(a) Arc Definition  (b) Chord Definition 
Figure F2 Degree of Curvature 
Arc definition is used in highway and street design while the Chord definition is used in railroad design. Because each definition differs, there is a slightly different radius relationship for each:
Equation F4  Equation F5 
R: Radius (ft) 
Degree of curvature is an exclusively English units system attribute as there is no 100.00' equivalent in the metric system. Because of this, we won't use it here in the COGO section.
b. Sectors; Segments
Sectors and segments are parts of a circle and used to compute areas enclosed by curvilinear boundaries.
Figure F3  Figure F4 
Equation F6  Equation F7 