A Strange Cevian

Geometry Level 2

Triangle ABCABC is such that AB=13,BC=14,AB = 13, BC = 14, and CA=15.CA = 15. A point DD on BCBC is placed such that AB+BD=AC+CD.AB + BD = AC + CD. Let XX be the intersection of ADAD with the incircle of ABCABC closest to A.A. Find the length of BX.BX.

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