(1) Because AMC is a right triangle and M is a right vertex.

So I'm vertical c1m.

Because ABC-a1b1c1is a regular triangular prism.

So ABC is a regular triangle.

BB 1 vertical ABC

So BB 1 vertical AM

And because BB 1 intersects with c1m.

So AM is perpendicular to the surface BCC 1B 1.

So AM is perpendicular to BC

So AM is the center line of ABC.

So m is the midpoint of BC.

ABC is a regular triangle, which mainly proves that AM is perpendicular to AM, so AM is a vertical line, that is, the middle line.

(2) Make a vertical line from point C to C 1M, with the focus of d, that is, CD is perpendicular to c1m..

Because AM is perpendicular to the surface BCC 1B 1.

I am also a vertical CD.

And because C 1M vertical CD.

AM and C 1M intersect at m.

So the vertical plane of CD AMC 1

That is, CD is the distance from point C to AMC 1.

The length of CD should not be difficult to calculate.