Because this is a right triangle ABC (Pythagorean Theorem), the side corresponding to angle C must be the diameter.
Because point C is fixed on the triangle ABC, the key point is point E, which slides from point A to point B, so when is the circle drawn smallest? That's when CE is perpendicular to AB. At this time, CE is also the diameter of a circle, so CE=6*8/ 10=4.8=MIN(QD).