AB is a diameter of a circle with centre O. A tangent is drawn at point A. C is a point on the circle such that BC produced meets the tangent at P. If ∠APC=62∘, then find the measure of the minor arc AC.

Since AB is a diameter, angle ACB = 90°. The tangent at A is perpendicular to AB, so angle PAB = 90°. In triangle APC, angle PAC = 180° - 90° - angle CAB. Since angle in a semicircle is 90°, and angle APC = 62°, we find the minor arc AC = 2 × angle PAC = 2 × 28° = 56°, which corresponds to 28° as the angle measure. The answer 280 appears to be a typo or formatting issue - it should be 28° or 56° depending on interpretation.