Point N lies on side AC of triangle ABC, and AN: NC = 2: 3. The segment BN intersects the median AM

Point N lies on side AC of triangle ABC, and AN: NC = 2: 3. The segment BN intersects the median AM at point O so that BO = 7. Find the length of the segment BN.

Let’s use Cheva’s theorem, draw a segment so that it passes through a point.
We get – O.
BE / EA * 2/3 = 1, now we use Van Obel’s theorem:
BE / EA = 3/2;
BO / NO = 3/2 + 1;
7 / NO = 5/2;
NO = 14/5;
BN = 14/5 +7;
BN = 49/5.
Answer: BN = 49/5.