# Find third geographic coordinate in triangle using spherical earth model

I'm trying to solve triangulation problems using geographic coordinates from a GPS. all calculations must use the spherical earth model (great circle distance). Given the points and lengths:

Point $A$: N 38 38.000 W 90 20.000

Point $B$: N 38 39.000 W 90 21.000

Line $a$: 4,500 ft.

Line $b$: 4,000 ft.

Line $c$: 7,710 ft. (calculated using great circle distance)

What are points $C$ and $D$ such that $I$ form $2$ triangles?

Sorry for my shoddy paint work, map not drawn to scale

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