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The "Proof of existence" appears to apply to a figure with different lettering than the one at the top of the page. For the proof to apply as written, the diagram should have the letters M and N interchanged, and the letters A, B, and C rotated around the triangle, i.e. the point now labelled B should be relabelled A, the point now labelled C should be relabelled B, and the point now labelled A should be relabelled C. Alternatively one could replace the letters in the proof to apply to the existing diagram. As it stands, however, it is confusing and unacceptable.
Proof of existence
O.K so PMB is a right angle (perpendicular from P to CB) So by Thrales theorem we can draw a circle through P,M and B with PB a diameter. We then note that BNP is also a right angle so N also lies on the circle and BNMP is a cyclic quadrilateral. Took me 15 minutes to work this out (timed it). Am I stupid or is the explanation a bit wanting? — Preceding unsigned comment added by 194.176.105.144 (talk) 14:31, 30 July 2013 (UTC)
Point D in the conclusion of the second generalization has not been defined. Loraof (talk) 02:48, 12 July 2017 (UTC)
I believe that the two IP editors 27.67.36.135 (talk · contribs) and 2405:4800:1486:CBF0:5519:B8D1:75D9:3096 (talk · contribs) who have recently been edit-warring to include the minor generalizations of Dao Thanh Oai are sockpuppets of User:Eightcirclestheorem, previousy blocked for sockpuppetry in connection with self-promotion of Dao's results on other articles in Wikipedia. They are now blocked. See also multiple AfDs on articles promoting Dao: Wikipedia:Articles for deletion/Dao Thanh Oai line, Wikipedia:Articles for deletion/Dao's theorem, Wikipedia:Articles for deletion/Dao's six point circle, Wikipedia:Articles for deletion/Dao's theorem on six circumcenters, and Wikipedia:Articles for deletion/Dao six-point circle. —David Eppstein (talk) 16:30, 31 July 2017 (UTC)
... is no such thing, nor has it been for the 23 months it had been allowed to remain.
See [1]
216.213.165.204 (talk) 08:30, 4 September 2022 (UTC)