Question

a sketch in which a line is drawn tangent to an arc will only be parametric if... a. the coordinates of the tangency point are determined at the moment the geometric condition is established, and the tangency condition itself is also saved. b. the coordinates of the tangency point are determined at the moment the geometric condition is established, but the tangency condition itself is not saved. c. the coordinates of the tangency point are determined before the geometric condition is established, but the tangency condition itself is not saved. d. the coordinates of the tangency point are determined before the geometric condition is established, and the tangency condition itself is also saved.

Explanation:

To determine the correct option, we analyze the concept of parametric tangency in geometry (specifically in the context of technical drawing or geometric construction). In parametric tangency for a line tangent to an arc, the geometric condition (like the perpendicularity of the radius to the tangent at the point of tangency) is established at the moment the tangency is determined, and the tangency condition (the coordinates of the tangency point) is also saved. Option A matches this description: it states the coordinates of the tangency point are determined at the moment the geometric condition is established, and the tangency condition itself is also saved. Option B says the tangency condition is not saved, which is incorrect. Options C and D say the coordinates are determined before the geometric condition, which is contrary to the correct geometric process (the geometric condition defines the tangency, so the coordinates are determined when the condition is established, not before).

Answer:

A. The coordinates of the tangency point are determined at the moment the geometric condition is established, and the tangency condition itself is also saved.