I can see this going 25 pages

I got the smartest guy I work with on it. We'll get it done!

to me math is plus minus multiply divide
The rest of that stuff is Greek to me

No matter how mathematically gifted, he will NEVER solve it if you ONLY have two endpoints to work with. You're asking for a "curve-fit" and that's an aesthetic action.
The origin point for a radius that connects two dots is an infinite number of points (but all along a line with varying angles to each endpoint you provided).
You will have to provide a third point on the proposed arc in order to write a finite equation - or allow some sort of assumption to be considered in the equation.

Here's a description of why there is not a single solution. Get yourself two paper plates. Lay one over the other offset in some amount, say two inches, such that they aren't stacked neatly. I bet you will agree that the centers of the two plates are not the same point - they're offset because you didn't stack the plates neatly. That center is the x2/y2 point you seek. Now, look at the edges of the plates - they cross over one another at two points. One of those is x/y, and the other is x1/y1. So, the two points you gave as fixed ARE parts of both arcs, and those arcs are parts of two different circles with two different centers. This is why an equation cannot be written to solve for a single unique radius origin (x2/y2) that you ask for. There are actually MANY answers that fit what you ask, not just a single point. Show your "smart guy" this. I'm betting you'll get an "ahhh" from him.

Well, you're correct! ....as the Greeks DID do a lot of advanced mathematics.

WOW! I didn't understand a single thing in that post but dam, it sure read purty.

I goofed a bit on one aspect of it, hopalong. I'm surprised you didn't catch it!

"The origin point for a radius that connects two dots is an infinite number of points (but all along a line with the same angle varying angles to each endpoint you provided).

Now THAT is an award winning OT solution!

OK, back to being serious. I have a question for the OP. Does the tool or program you are using have any higher functions that will calculate the rotation of a vector?

One solution I would propose is that we try out an assumption of choosing a radius R for the circle that will connect the points of the arc. This gives us a third point so we can solve the problem. We would set this value R to be the distance between the two points you have provided. I can't write equations in this simple forum text, so I'm a bit hampered. Solve for the distance between the two points using a right triangle and Pythagoras' theorem. The line between your points will be the hypotenuse.

Create a vector (or if you are lucky with your program) define a vector at one point of length R. Rotate that vector 60 degrees to define the point you are asking for. You'll have to rotate it twice (+60 deg & -60 deg) so that you can choose which side of the two endpoints you wish for that new point to be. The equation can't tell what you want, so you'll have to look at both solutions.

If you can't do vectors, then solve for the 3rd point in an equilateral triangle (where your two existing points are the other endpoints of the triangle). Once again, you'd get two answers (one on either side of the two existing points), so you'll need to choose the one that will give the desired radius effect.

I'll have to start charging back-me-up favors if you need help with the above steps as that gets into more time.

Maybe I missed it, but what size is the radius?

update, my solid edge api has a method to add by start along end. so I have start and end, I need a point on the arc.

dude, y'all lost me at origin point, math is not my strong point by any means.

so now I need to solve for the point at the green arrow.

X2= 2.174
Y2= -1.174

I need to know what the angle of the two tangent lines are