5.2.4.45 Various problems on the plane

Condition: On the sides \( A C \) and \( A B \) of 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 relation \( B O: O M \).