During which stage of mitosis do the chromosomes attach to a spindle microtubule at the centromere?

During mitosis, the stage when chromosomes attach to spindle microtubules at the centromere is metaphase. During this phase, the chromosomes, having already replicated and condensed, align at the cell's equatorial plane due to the action of spindle fibers. Each chromosome's kinetochores, which are protein structures on the centromere, serve as the attachment points for the spindle microtubules. This precise alignment is crucial for ensuring that, when the chromosomes are pulled apart in the next stage (anaphase), each daughter cell will receive an identical set of chromosomes.

In contrast, prophase involves the condensing of chromatin into visible chromosomes and the formation of the mitotic spindle, but it is during metaphase that the actual attachment to microtubules occurs. Anaphase is characterized by the separation of sister chromatids, and telophase marks the reformation of the nuclear envelope around the separated sets of chromosomes, without the attachment to spindle microtubules.