Using a formula to calculate latitudes coordinating with given longitudes to make a circle

I am plotting out the latitude and longitude coordinates of a circle in Excel. Essentially, I want the coordinates, when mapped out, to make a 45 mi radius circle which I can then apply to any latitude and longitude.
What I have is a list of all the longitudes, doubled, for which I want a latitude. I also have the northernmost latitude point (representing the top of the circle) as a starting point. The intended path of the longitudes of the circle is in a clockwise direction.

What I'm looking for is a formula that I can use in coordination with the longitudes to give me the corresponding latitude. I know if I go with a fixed formula (latitude +/x) then I'll end up with a diamond. I'm assuming I'll need to convert them to radians, perhaps use the haversine formula, and convert them back to degrees but that's where I get lost.

In the example file, the reference points [Latitude, Longitude] are:
Origin: [38.0, 0.0]
North: [38.65217, 0.0]
East: [38.0, 0.83333]
South: [-38.65217, 0.0]
West: [38.0, -0.83333]


Calculating Latitudes - Copy.xlsx

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You assume that 0.5 miles has a constant latitude difference, but that is not correct. Longitudes are much closer together at the poles than at the equator. Moreover, the 4 given reference points do not lie on 1 circle, the distance north-south in the given example is much greater than east-west. The 4 given reference points are all located around the equator and there the longittude difference and latitude difference per distance are almost equal. But in your example workbook, these points differ significantly. To construct a circle on a sphere, it is useless to assume a fixed distance between the degrees of longitude per unit of distance. Even within the circle, this distance varies.

Calculating points on a sphere that form a circle requires a completely different approach. I would use the following input parameters as input parameters: * longitude and latitude of the center of the circle, * radius of the circle and radius of the sphere on which the circle should be constructed. Or use as parameter 3 points on the sphere through which the circle must pass. On a sphere you can almost always construct 2 circles that pass through 3 given points on the sphere. I don't cough up the necessary calculations myself and still require the necessary effort for me.

I'm not as concerned with the variation in longitude distances since it would likely be immaterial for my purposes

In that case its very easy to construct the circle:

Please try on sheet reference point:

Put in F1 the number of points you want to use to construct the circle

Latitudes: Please try in E3:

Formula:

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Longitudes: Please try in F3:

Formula:

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