# A Strange Cevian

Geometry Level 2

Triangle $$ABC$$ is such that $$AB = 13, BC = 14,$$ and $$CA = 15.$$ A point $$D$$ on $$BC$$ is placed such that $$AB + BD = AC + CD.$$ Let $$X$$ be the intersection of $$AD$$ with the incircle of $$ABC$$ closest to $$A.$$ Find the length of $$BX.$$

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