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How to construct a hexagon, a regular 6-sided polygon, given one side?
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| 1. |
| Start with the construction of an equilateral triangle with the same given side.
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| 2. |
| Draw a circle with the center at the top of the triangle, and a radius equal to one side of triangle 1.
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| 3. |
| Draw an arc with its center at the left angular point of triangle 1, and a radius equal to one side. It must intersect circle 2 twice (once in the angular point on the right).
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| 4. |
| Draw the connecting line between the center of arc 3 and the second intersection of it with circle 2.
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| 5. |
| Draw the connecting line between the last mentioned intersection (4) and the top of triangle 1, and extend it until it intersects circle 2 a second time.
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| 6. |
| Draw the connecting line between the right angular point of triangle 1 and the last mentioned intersection (5).
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| 7. |
| Extend the left side of triangle 1 until it intersects circle 2 a second time.
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| 8. |
| Repeat this for the right side of triangle 1.
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| 9. |
| Draw the connecting line between consecutive intersections of circle 2, first between intersections 5 and 7.
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| 10. |
| Next between intersections 7 and 8.
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| 11. |
| Finally between intersections 8 and 3.
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| 12. |
| Lines 4, 6, 9, 10 and 11, together with the base-line of triangle 1, form the hexagon to be constructed.
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