Point coordinates on curved spline

Hi guys.

I am banging my head to the wall for some time now with this issue.

As a simplified version, I have a perfect circle and I need to find midpoint coordinates between two vertices. In this case:

A is a vertex with coordinates [0, 0]

B is a vertex with coordinates [500, 0]

A1 is OutTangent of point A with coordinates [138, -138]

B1 is InTangent of point B with coordinates [362, -138]

The goal is to find midpoint coordinates.

Again, this is very simple scenario. Other times tangent will be different lengths and shapes will be random as well, so I'd like to wrap my head around finding coordinates based on 2 vertices and InTangents and OutTangents.

Thanks in advance.

UQg,