Construct an equilateral triangle, square, and regular hexagon inscribed in a circle.
Construct an inscribed regular hexagon by stepping the radius
Problem
A circle is centered at \(O\). Starting at \(A\), keep the compass opening equal to the circle radius. Construct the inscribed regular hexagon by stating the compass width, vertices in circular order, central angles, connection order, and side-radius result.
Big Picture
What this problem is really about
Stepping a fixed compass opening around a circle links three facts at once: equal chords, equal central angles, and eventual closure. We’ll derive the angle created by one radius-length chord, check how many identical steps fill a full turn, and then follow the circumference order when connecting the marks.
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