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proof of nine point circle?

pics or it didn't happen. —Preceding unsigned comment added by 70.36.140.140 ( talk) 19:09, 3 January 2010 (UTC) reply

The following "construction" was removed as inadequate: Construction

Starting out with a right hyperbola, we can find a focus and its reflection on the line of reflection y=x (Reflection Symmetry). Given these two points, we use a drafting compass to find two alternate points on the right hyperbola. When you draw a line through one of those points and the constructed foci point you get another point on the hyperbola.

A triangle can be constructed where all three vertices are the points previously constructed. Also the side constructed by the two points found using the drafting compass goes through the origin. Using this triangle, angle bisectors are constructed to produce the orthocenter. Also, by using this triangle the midpoint of each side is determined.

Once you have constructed the angle bisectors and the midpoints of each side, you now have all the points needed in order to construct the nine-point circle.

Similarly given a rectangular hyperbola, this same nine-point circle can be constructed using the same methods used above when complete; the rectangular nine-point hyperbola would look like this.

A well-executed diagram would be appreciated. Rgdboer ( talk) 02:13, 10 December 2014 (UTC) reply