circular curve fitting

[swah2000]

As the coordinates of two tangent points are fixed by some constraints. I would like to fit a circular curves to joint them together. If begin radius say is 80m. How can I find the second radius which shown in attached file ?

 

[IRstuff]

You don't seem to have fully defined all your constraints; is it supposed to be smooth curve? To what degree?

What was the rationale for picking 80?

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[IRstuff]

Is this for school? Student posting is forbidden.

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[Ingenuity]

One method would be to use the Sine Rule and Cosine Rule:

Solving, as follows:

 

[Ingenuity]

Doing it graphically in CAD is easier using the AutoCAD 'ARC' command with 'Continue' arc.

Knowing the end point of first arc (R₁ = 80000), and knowing the PT (tangent point of the end of the second arc) 'ARC Continue' will continue a tangent arc from the PCC (compound curve point) to the PT, then use 'dimension' to obtain the drawn radius.

I also get R₂ = 41772 using CAD.