measuring intersection angle between circle and line with thickness

[lathe1]

In the attached drawing, it is required to find the angle 71 resulting from the intersection of the arc with the line from the outside and the arc with the line from the inside, noting that the thickness is 5 cm. The problem is that I do not know the location of the intersection of the internal arc with the internal line to form a vertical angle 71. The intersection point is required by mathematical equations or by visual basic

Finding the point of intersection of the interior arc with the interior vertical line and the angle measure 71 by mathematical equations or by visual basic

 

[blamocur]

Can you figure out the equation for the outer arc? How about for the inner arc?

 

[lathe1]

I can calculate the length of the outer arc and the geometric center of the outer arc
The center of the arc is 27.5
The length of the arc is 129.2
I can do that through computer-assisted design
Autocad

 

[Dr.Peterson]

I can calculate the length of the outer arc and the geometric center of the outer arc
The center of the arc is 27.5
The length of the arc is 129.2
I can do that through computer-assisted design
Autocad

But you want to calculate everything by your own calculations, right? Or am I misunderstanding?

I'd like to see how much you are able to calculate using whatever methods you want to use for the 71 degrees.

Is the angle you want the angle of the line joining the two intersections?

I have found that angle using formulas found here. I found the radius of the outer arc, subtracted 5 to get the radius of the inner arc, then found the sagitta (h) for the inner arc, from which I could find the vertical distance; the slope of that line is 19.2 degrees, whose complement is 70.8 degrees. So that's probably what you want.

 

[lathe1]

thank you