Is there a catalogue of triangles in which one might find for instance the name of the right angle triangle with an angle of approx 35 degrees in which the altitude, median and side bisectors intersect at a point? Or in which the diameters of the incircle through the touch points end on Euler's line? Ideally this catalogue would list lots of interesting triangles, their dimensions, method of construction, names etc. Despite several hours searching I cannot find such a catalogue. The closest I found is the list of triangle centres, but these work for any triangle. Thanks for your help.
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I think you need to look into books devoted to the specific subject. I have not read or browsed any of the linked books, but may you could find what you want in there. You may still find that there is a place for one more book about the subject...Here are 2 books I came across, again, I did not read any of them:http://shop.ukmt.org.uk/ukmt-books/the-geometry-of-the-triangle and http://www.amazon.ca/Secrets-Triangles-Mathematical-Journey/dp/1616145870/ref=sr_1_3?s=books&ie=UTF8&qid=1453073067&sr=1-3&keywords=the+geometry+of+the+triangle – NoChance Jan 17 '16 at 23:27
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I have looked through the "The Secrets of Triangles" - a delightful book. Page 240 lists methods of constructing 90 triangles but this does not catalogue the triangles. – prb Jan 18 '16 at 12:34