Getting a point from a point, length and angle

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Using the diagram below, if we know the coordinates 'point A' and 'point B' as well as side lengths a,b,c. Is it possible to get the exact coordinates for points D & C that would also function as expected if sides a and b are not of equal length

https://i.stack.imgur.com/FZUX6.jpg

EDIT: Solved, thanks for the proof example David K. So simple in practise :)