Final answer:
Option D is incorrect because drawing a line segment between the top intersection point of the two circles and the radius of the first circle does not necessarily form the side of an equilateral triangle inscribed in a circle.
Step-by-step explanation:
To determine which of the given directions for constructing an equilateral triangle inscribed in a circle does not work, we need to visualize the basic properties of such a triangle and its relationship to the circles. An equilateral triangle inscribed in a circle has all its vertices on the circumference of the circle, and the sides of the triangle are equal in length.
Option A suggests drawing a line segment from the endpoint of the diameter of the first circle that is not also the radius of the second circle to the bottom point of intersection of the two circles. This is one correct method to form the side of an equilateral triangle. Similarly, option B, which involves drawing a line segment between the endpoint of the diameter and the upper intersection point of the two circles, also forms a side of the equilateral triangle correctly.
Option C suggests drawing a line between the intersection points of the two circles. This will correctly create the base of the equilateral triangle. However, option D is incorrect because it states to draw a line segment between the top intersection point of the two circles and the radius of the first circle. This would not generally create the side of an equilateral triangle unless the radius mentioned coincidentally falls on another vertex of the triangle, which typically is not the case. Therefore, option D would not represent directions to construct the sides of the equilateral triangle.