Two tangents drawn from an external point P touch a circle at A and at B. The minor arc AB measures 104°. What is the measure of ∠APB?

The two tangents cut off the minor arc AB = 104° and the major arc AB = 360° − 104° = 256°. The external-point rule gives ∠APB = ½(256° − 104°) = ½ × 152° = 76°. The familiar shortcut agrees: the angle between two tangents is the supplement of the central angle, 180° − 104° = 76°. The trap 104° copies the arc straight across as though P were the centre, 128° halves the major arc alone, and 52° halves the minor arc.