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Bottema's Theorem (1938)

As is often the case in mathematics, though given Bottema's name, the result was also known elsewhere at about the same time, and already known and mentioned earlier. It is an exercise in C V Durell's New Geometry for Schools (1939), p. 287, Q26. Earlier still, it is in J W Russell's Sequel to Elementary Geometry (1907), p. 34, Sect 6 - a worked example. The converse result is an exercise in a French textbook, Traite de Geometrie by E Rouche and C de Comberousse (1900) vol 1, p. 395, Q254. This is the 7th edition, and the result might have appeared even earlier.

Can you generalize further? Go to the following for some generalizations: Some generalizations