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    Re: Finding The Symmedian
    From: Andrew Nikitin
    Date: 2010 Dec 24, 09:12 -0800

    Hello, Herbert.

    "Did you literally just read to the end of page 38 or did you follow the
    argument at least to fig. 4 in the middle of p. 39?"

    I kind of followed, pages 38 and 39 with fig 3 and 4 ("kind of" because I can't read language it is written in). I got the concept, I just did not see the relevance of 90-45-45 triangle in this construction.
    Your later explanation and sketch clarified that for me very well. Thank you very much.

    The figure needs to be drawn in black on transparency. Lowest horizontal line should coincide with the edge.

    Red is an example cocked hat. The device is overlaid on top of it so that left and right vertexes of hat's horizontal side lay on the diagonal lines (closely spaced parallel lines on a tool serve as guides to keep lower edge of a tool parallel to hat's side).

    In this position the lower edge of a tool is parallel to the lower edge of a hat. The spacing between them is equal to half the hat's side. Draw line along the lower edge of the tool. Repeat for the other side adjacent to same vertex. Connect intersection point to the vertex to obtain a line where symmedian must be.

    The drafting triangle on the link that you posted (http://www.schulfabrik.de/shop-445-aristo-geo-dreieck.html) has something resembling this pattern: there are 2 dashed diagonal lines, emanating from the middle of the top side, as well as several parallel guides. Is that what you had in mind?

    (BTW, since the distance from hat's side has to be *proportional* to the side's length, the slope of emanating lines does not have to be 45. It can be made more shallow. Slope of atan(1/2)~26.6 will allow to draw parallels at a distance equal to quarter of a length)

    Andrew Nikitin.
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