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In triangle ABCABCABC, AB=41 AB = \sqrt{41} AB=41 and AC=164 AC = \sqrt{ 164} AC=164. The internal angle bisector of BAC BACBAC meets BCBCBC at DDD. Given that lengths ADADAD and DCDCDC are positive integers, what is the value of AD+DCAD+DCAD+DC?
This problem is proposed by Sreejato.
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