Problem preview

G-CO.13 Core M1-036-R02-V03

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 \(Q\). Starting at \(N\), its radius is stepped around the circumference to mark \(\text{six}\) points \(N,~R,~S,~T,~U,~\text{and}~V\) in order. Construct an inscribed equilateral triangle by stating the vertices, central spacing, connection sequence, and result.

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vertices = N,S,V; central spacings = 120°,180°,60°; connection = N-S-V-N; result = equilateral

vertices = alternating N,S,U; central spacing = 120°; connection = N-S-U-N; result = inscribed equilateral triangle

vertices = all six; central spacing = 60°; connection = all marks; result = triangle

vertices = adjacent N,R,S; central spacing = 60°; connection = N-R-S-N; result = equilateral

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Curriculum context

Course: Math I
Standard: G-CO.13
Category: Geometry
Domain: Congruence
Objective: Construct an equilateral triangle, square, and regular hexagon inscribed in a circle.
Problem type: Construct an inscribed equilateral triangle from six radius steps