Curves of land

In Texas, distances always on the bottom of the list of boundary re-construction. It is below found monuments and bearings.

However, when reconstruct a curve, usually what I found on the ground are two tangent lines, the PC and PT monuments are there, it fits with what is called for in the chord distances, but it will not fit with the tangent line, meaning the delta angle of the curve is not the same with what called for in the design plan.

In that case, there are two scenarios to follows: I can hold the monuments for PC and PT, intersect distance to get the radius point, and make a non-tangent arc; or I can hold the the tangent lines, and create the tangent arc, but then the PC and PC of this tangent arc will not be right at the found monuments anymore.

Either of the choices make me cringe my teeth. Non-tangent arc? We all know that is not  the intention when the curve is created. However, ignore the found monuments for PC, PT? It just go against everything I was taught. If it was a line, I'm sure nobody would bat an eye and just hold monuments, no matter what the bearing or distance, but how is this different with a curve?

The thing is, who says we have to keep the radius as constant? Radius is a distance for me, and distance is the lowest on the pole. I know radius comes from degree of curve. But then again, bearings / angles are just only above the distance and below the found monuments. So why do people keep radius and distance? Why don't the monuments keep and create a new tangent radius?

I can find no solution for this. Is there a case about this already and we just follow the example.