Construct an equilateral triangle, square, and regular hexagon inscribed in a circle.
Construct an equilateral triangle on a segment
Problem
Segment \(AB\) is given. Circles centered at \(A\) and \(B\) with radius \(AB\) meet at \(C\) and \(D\), and \(C\) is the specified intersection. Complete the equilateral-triangle construction by stating the radius and centers, intersection used, sides to draw, and resulting side equality.
Big Picture
What this problem is really about
Two equal-radius circles turn one given length into two certified distances without measuring. We’ll use the base as the shared compass opening, interpret a common circle point through the radius definition, and then decide which connections complete the figure while preserving all three required side equalities.
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