Make Bezier Curve Control Points At Right Place On The Map

I wanna draw a bezier curve between two location points. I can draw some curve following some answers on stackoverflow, but the point for bezier control points are placed wrong for

Solution 1:

Scale in km(miles) per degree is different for latitude and longitude, so for usually used projections scale differs by factor f=Cos(latitude), map is anisotropic.

So you can:

1) generate control points Bezier curve in screen coordinate system (pixels) or 2) build correct middle perpendicular in Lat/Lon system using formulas from this page - find middle point at big circle arc, find bearing in that point, find perpendicular bearing, build point at some distance from middle at perpendicular bearing