Mathcad Community Challenge July 2022 - Area of a Spherical Triangle

This month's challenge is another geometry-based challenge - but it's non-Euclidean geometry. Given the following three points on a circle of radius 10 units, calculate the area of the spherical triangle:

(5.339, 6.948, 4.819)

(-4.018, -3.703, 8.375)

(6.455, -6.679, -3.705)

(Note that the point coordinates are rounded to three decimal places.)

Optional:

• Can you write a program or function that calculates the area for any three points on the surface?
• Is there a symbolic evaluation for three generic points (a,b,c), (d,e,f), and (g,h,k)?

Here is a 3D model in Creo 9 of the sphere and points:

Find the Mathcad Community Challenge Guidelines here!

Edit: the coordinates of the second point were incorrect. Wildly incorrect. I have no idea how I wrote down the wrong numbers.