I know the base ABCD in an irregular pyramid. I know all angles at the top. Is it possible to determine the sides OA, OB, OC or OD?

Known are:
lengths: AB, AC, AD, BC, BD, CD
angles: AOB, AOC, AOD, BOC, BOD, COD and all in the base plane (ABC, ABD etc).
AD is parallell with BC.

My problem is that for every triangle involving O, I only have 1 side and 1 angle.

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