It is known that in triangle ABC side AB = 7, AC = 4. Find the ratio in which the bisector of angle A

It is known that in triangle ABC side AB = 7, AC = 4. Find the ratio in which the bisector of angle A divides the median drawn from the vertex B. In your answer, indicate the ratio of the larger segment to the smaller one.

Let BM be the median, AE the bisector, BM and AE intersect at point O.

Consider the triangle ABM: AB = 7 (by condition), AM = 2, since the median BM divides the AC into two equal parts.

By the property of the angle bisector: the angle bisector of a triangle divides the opposite side into segments proportional to the adjacent sides.

Therefore, BE refers to MO as AB to AM.

BE / MO = AB / AM = 7/2.