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20070317, 05:44 #1
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Calculate center of a triangle (XL 2003)
This is more of a geometry question, but I'm not sure where to ask. I'm trying to calculate the coordinates in Excel for the center of a triangle, the orthocenter I believe.
Is there a formula already in Excel to return the x, y coordinates of the center when given the x, y coordinates of the three vertices?

20070317, 10:06 #2
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Re: Calculate center of a triangle (XL 2003)
It depends on what exactly you mean by the "center" of the triangle. There are several points that could be called the center:
<UL><LI>The intersection of the medians, i.e. the lines from a vertex to the midpoint of the opposite side. This intersection is called the centroid, and it is also the triangle's center of gravity: if you cut a triangle out of a material of uniform density and rest the triangle on a pin at the centroid, it'll be in balance.
<LI>The intersection of the altitudes, i.e. the lines from a vertex perpendicular to the opposite side. This is called the orthocenter.
<LI>The intersection of the angle bisectors.
<LI>The center of the circle passing through the three vertices, the circumcenter.[/list]See Triangle  wikipedia entry.
The centroid is the easiest to calculate: the xcoordinate is the average of the xcoordinates of the vertices and the ycoordinate is the average of the ycoordinates of the vertices.
So with the vertices in A1:B1, A2:B2 and A3:B3, the centroid is given by =AVERAGE(A1:A3) and =AVERAGE(B1:B3)

20070317, 10:50 #3
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Re: Calculate center of a triangle (XL 2003)
Here is a spreadsheet to get the "OrthoCenter"
Steve

20070319, 18:25 #4
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Re: Calculate center of a triangle (XL 2003)
Thanks all  these will get me started!