5.2.4.45 Various Problems on the Plane

Condition: on the sides \ (a c \) and \ (a b \) the triangle \ (a b c \) the points \ (m \) and \ (n \) are taken respectively so that \ (a m: m c = 9: 1, a n: n b = 4: 5 \). Find the relationship \ (b o: o m \).