In triangle ABC, internal bisector of angle A intersects with BC at D. Let E be a point on [CB such that \left|DE\right|\equal{}\left|DB\right|\plus{}\left|BE\right|. The circle through A, D, E intersects AB at F, again. If \left|BE\right|\equal{}\left|AC\right|\equal{}7, \left|AD\right|\equal{}2\sqrt{7} and \left|AB\right|\equal{}5, then ∣BF∣ is<spanclass=′latex−bold′>(A)</span> 575<spanclass=′latex−bold′>(B)</span> 7<spanclass=′latex−bold′>(C)</span> 22<spanclass=′latex−bold′>(D)</span> 3<spanclass=′latex−bold′>(E)</span> 10 geometryangle bisectorsimilar triangles