why does** ac** cuts** mc** at its lowest point?

there is a close relationship between AC curve and MC curve.

MC=(change)TC/(change)Q and AC=TC/Q;Where TC=Total Cost and Q=output

when MC<AC,then AC falls

when MC=AC then ac is constant

when MC>AC then ac rises

MC Curve lies below AC Curve and then rises

therefore, MC curve always intersect AC at its lowest point