Been doing some A2 revision courses this holidays and this question came up. In the last two November A2 exams there have been multiple choice questions concerning the point on the Total Cost curve when MC, AVC, and ATC are at their lowest point. In the graph note the corresponding points on the Total Cost. They usually ask you where on the Total Cost line is the lowest point on the MC curve/AVC curve etc.
MC cuts ATC and AVC at their lowest points. The firm will supply where the price is greater than or equal to MC. Thus the individual firm’s supply curve consists of the firm’s MC curve, but only the portion above AVC . The reason for this is that where P=AVC the firm will shut down operations because they are barely covering avoidable costs.