Line AB with point C between A and B, with a circle drawn from center C with a radius CB and diameter DB, where D is between A and C; point E between C and B, with a circle drawn with center D and radius DE; another circle is drawn with center B and radius DE to create an equal sized circle as circle D; circles B and D intersect at H above line AB and G below line AB, and line HG is constructed through C.
a Inscribed regular hexagon
b Inscribed equilateral triangle
c Perpendicular line through a point off a line
d Perpendicular line through a point on a line

  d.  Perpendicular line through a point on a line

Step-by-step explanation:

We presume you're looking for a description of line HG.

The construction makes points H and G equidistant from points D and B, and it puts point C on the line HG. This makes HG perpendicular to AB, and it makes HG contain point C. Thus we have a perpendicular through a point on a line.

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Nothing about this construction creates an equilateral triangle or hexagon. The perpendicular is through points H and G, which are off the line AB, but we did not start with those. A perpendicular through an off-line point is constructed differently.

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