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They are triple third cousins seven times removed.
The nearest common ancestors between the Duke of Braganza and John William Friso, Prince of Orange are Maurice, Landgrave of Hesse-Cassel and his wife, Countess Juliane of Nassau-Siegen/Dillenburg.
Since they are the nearest common ancestors of the Duke and JWF, they *should* also be the nearest common ancestors between him and everyone descended from JWF.
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