Construct an equilateral triangle, square, and regular hexagon inscribed in a circle.
Construct an inscribed equilateral triangle from six radius steps
Problem
A circle has center \(O\). Starting at \(A\), its radius is stepped around the circumference to mark \(\text{six}\) points \(A,~B,~C,~D,~E,~\text{and}~F\) in order. Construct an inscribed equilateral triangle by stating the vertices, central spacing, connection sequence, and result.
Big Picture
What this problem is really about
The six radius steps create a circular grid of equal central gaps, but the requested polygon uses only part of that grid. We’ll determine how many basic gaps each of its three sides must span, identify a consistently spaced triple of marks, and convert equal central angles into equal side chords.
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