In an acute-angled triangle MNP, the bisector of angle M intersects the height NK at point O, with OK = 9cm.

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

1) From point O we draw a perpendicular to the side MN and take the point behind T.
2) OТ-distance from point O to MN.
3) Triangles MOT and MOC are equal in side and two adjacent corners.
4) Angle TMO = OMK since MO-bisector of angle M.
5) MO-common side.
6) Triangles MOT and MOC are equal in hypotenuse and acute angle.
7) From the equality of the triangles, it follows OK = OT = 9 cm.
Answer: 9 cm.