Area depends on the square of the radius (A = πr²). When radius becomes 0.9r (10% reduction), new area = π(0.9r)² = 0.81πr². The reduction is 1 - 0.81 = 0.19 = 19%. Option A (10%) would be true for circumference, not area. Option C (20%) ignores the squared relationship.
The area of a circle is proportional to the square of its radius. If the radius is reduced by 10% (becoming 0.9 of the original), the new area becomes 0.9² = 0.81, or 81% of the original — meaning the area is diminished by 19%, not simply 10% or 20%.