Labeling Tangent Length for simple curve or transition curve

[nirmal.maisuria]

Hello there,

I want to label tangent length in both the case mentioned below using "if" function.

Case-1 When there is simple circular curve. what is expression for external tangent length (pls see attached image 'length from point PC to PT?')

Case-2 When there is Spiral-Curve-Spiral. what is expression for external tangent length (pls see attached image 'length from point A to B ?')

[Kent1Cooper]

No offense intended, but I think those diagrams are badly drawn.  In the upper one, shouldn't the R radius lines be perpendicular to the PC-PT and PT-PT [another issue -- there are two  PT's] lines?  They're clearly neither perpendicular to those nor radial to the arc.  And shouldn't the smaller I/2 angle near PC be from the horizontal line to the PC-PT line, not to the arc?  In the lower one, are the "transition curves" supposed to be tangent  continuations of the "circular curve" at D and E?  They're clearly not.

It would be easier to picture the geometric relationships with better diagrams.

[nirmal.maisuria]

Thank you for response. But those diagrams are just for the reference.
Actual alignment have accurate parameters. I just want to label my
alignment at curve portion with External Tangent Length (mt.). My Alignment
consist Simple circular curve as well as transition curve for that I want
to use "if" function expression.

[TheCADnoob]

case 1 is the pythagorean theorem

for case 2 you need a function of the shape that is generating the non  circular arc. As its non circular it will not be scaleable (or rather be able to put into a function) without this information.