Math Problem Statement

Stella is using her compass and straightedge to complete a construction of a polygon inscribed in a circle. Which polygon is she in the process of constructing?

A circle is drawn with five arc markings that lie on the circle, with an additional point also marked on the circle.

A regular octagon A square A regular pentagon A regular hexagon

Solution

Stella is constructing a regular hexagon.

Here's the reasoning:

  • The problem mentions that there are five arc markings on the circle, which divides the circle into six equal parts.
  • Adding the additional point would complete the sixth arc, implying that the circle is divided into six equal arcs.
  • A regular hexagon can be inscribed in a circle by dividing the circumference into six equal parts, corresponding to the six vertices of the hexagon.

Thus, the correct answer is: A regular hexagon.


Would you like more details or have any questions about the construction process?

Related questions:

  1. How do you construct a regular hexagon using a compass and straightedge?
  2. What is the relationship between the number of sides of a polygon and its inscribed circle?
  3. How can you use a compass to find the center of a circle?
  4. How do the side lengths of a regular polygon inscribed in a circle relate to the circle's radius?
  5. How can you construct a regular pentagon using a compass and straightedge?

Tip: In a regular polygon, the central angle (angle at the circle's center) can be found by dividing 360° by the number of sides.

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Math Problem Analysis

Mathematical Concepts

Geometry
Polygon Construction
Circles

Formulas

360° / n (central angle for regular polygon with n sides)
Circumference = 2πr

Theorems

Polygon Inscription Theorem
Central Angle Theorem

Suitable Grade Level

Grades 6-8