The distance from the point M to the hypotenuse BC is the perpendicular MH, then the triangle CMН is rectangular.
Let us prove that triangles CAM and CHM are equal.
The hypotenuse of the CM in triangles is common, the angle AFM = НСM since CM, by condition, is a bisector, then the triangles CAM and СНM are equal in hypotenuse and acute angle, and then MH = MA = 8 cm.
Answer: From point M to segment BC 8 cm.
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