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