First, we need to know what the different parts of the construction
are. We will start with the Circumcenter, then go to the 9-point
center, followed by the First and Second Fermat points.
| The circumcenter of a circle is obtained by finding the intersection
of the three perpendicular bisectors of each side of the triangle. |
Drag points A,
B, and C
to see how different triangles have different circumcenters. |
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| The 9-point circle is constructed by drawing a circle
that passes through each of the midpoints of the sides of a triangle. |
Drag points A,
B, and C
to see how different triangles have different 9-point centers. |
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| The First Fermat point is found like this.
Start with one side of the triangle. Treat that side as the base
of an equilateral triangle on the outside of the original triangle.
It will have a vertex that was not on the original triangle. Connect
that point with the other original vertex. Repeat that for all three
sides of the original triangle. Where these three lines intersect
is the 1st Fermat point. |
Drag points A,
B, and C
to see how different triangles have different 1st Fermat Points. |
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| The second Fermat point is found in the same manner as the first, but
this time the triangles are drawn inward. |
Drag points A,
B, and C
to see how different triangles have different 2nd Fermat Points |
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| Finally, here are all four points together on one construction. |
Drag point A, B, or C to see how different triangles
still obey Lerster's Circle Theorem. |
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