In an acute-angled triangle MNP, the bisector of angle M intersects the height NK at point O.

In an acute-angled triangle MNP, the bisector of angle M intersects the height NK at point O. OK = 9. Find the distance from point to line MN.

The distance from point O to the side MN is the perpendicular OH.
Consider right-angled triangles MON and IOC.
∠HMO = ∠ KMO (MO is the bisector by the problem statement).
MO is the hypotenuse common to two triangles.
We get the third sign of equality of right-angled triangles (by hypotenuse and acute angle).
From the equality of the triangles it follows:
OH = OK = 9.
Answer: the distance from point O to the MN side is 9.