In triangle A B C, points D, E, and F are on sides B C, C A, and A B respectively, such that B F=B D=C D= C E=5 and A E-A F=3. Let I be the incenter of A B C. The circumcircles of B F I and C E I intersect at X \neq I. Find the length of D X.
In triangle A B C, points D, E, and F are on sides B C, C A, and A B respectively, such that B F=B D=C D= C E=5 and A E-A F=3. Let I be the incenter of A B C. The circumcircles of B F I and C E I intersect at X \neq I. Find the length of D X.