Problem preview
G-CO.13 Warmup M1-036-A12-V01

Construct an equilateral triangle, square, and regular hexagon inscribed in a circle.

Compare inscribed regular polygons in the same circle

Problem

Use the displayed polygons inscribed in equal-radius circles. Compare their central angles and side lengths.

Big Picture

What this problem is really about

Equal circle radii make this a clean chord comparison: the only changing ingredient is the central angle subtended by one side. We’ll compute each polygon’s share of a full turn, order those angles, and then use the same-radius rule that larger central angles subtend longer chords.

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Four variants of this problem type
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
Compare inscribed regular polygons in the same circle