Final answer:
The question appears to ask for the length of arc MC in a circle, given lengths of segments intersecting at point C. However, without more context or additional information (such as angle measures), it's not possible to give a numerical answer for the arc length MC.
Step-by-step explanation:
The question seems to be missing some necessary information to solve for arc MC directly. However, if we consider that ID and AM intersect at C and form part of a circle, and if we had the information that ID and AM are chords of a circle intersecting at point C, then to find the length of arc MC we would need to know the relationship between the chords and the arcs they subtend in the circle. In general, the length of an arc is proportional to the degree measure of the central angle that intercepts the arc. Without additional details, such as the measures of the associated angles or whether segments ID and AM form a right angle, it's not possible to provide a numerical answer for the arc length MC.
Based on the information provided about segments IC, DC, and AC, and the references to circular motion and arc length from the excerpts, we can infer that the problem may involve concepts like segment length, arc length, and possibly circle theorems or central angles.