#### Question

In the figure, \triangle ABC is a right triangle such that \angle C=90\degree ， BC=6， AC=8. Point P is the midpoint of AB. Taking point P as the vertex, construct \angle MPN so that \angle MPN=\angle A and the arms of \angle MPN intersect AC at points M, N respectively.

Find the length of CM when \triangle MPN is a right triangle

If \angle MPN rotates around point P, find the length of CN\cdot AM