Which is the correct geometrical interpretation of (1) radian?

Correct answer: When arc length equals radius

A radian is defined geometrically by a circle’s arc. If an arc has length s equal to the radius r, then the angle subtended at the centre is one radian. This follows from the relation s = rθ: setting s = r gives θ = 1. Therefore option A is correct. An arc equal to the diameter does not define one radian; it would give θ = 2 radians. An angle of 90° is π/2 radians, not 1 radian, and an arc equal to the full circumference subtends 2π radians, a complete revolution. Thus the key condition is equality of arc length and radius, measured in the same units.