"1) The Euler line points such as X(21) do not produce equilaterals. But, if X = t O + (1-t) H, t ∈ R, and Xa = X(FBcCb), Xb = X(FAcCa), Xc = X(FAbBa), then triangle XaXbXc is equilateral.2) Everything that has been said also holds for X(14).Best regards,Elias M. Hagos"
Let H=X(4)-Orthocenter of ABC. A 1 B 1 C 1 cevian triangle of H. B1 A , C1 A are reflections of B1, C1 on A. L A , line through B1 A , C1...
"1) The Euler line points such as X(21) do not produce equilaterals. But, if X = t O + (1-t) H, t ∈ R, and
ReplyDeleteXa = X(FBcCb), Xb = X(FAcCa), Xc = X(FAbBa),
then triangle XaXbXc is equilateral.
2) Everything that has been said also holds for X(14).
Best regards,
Elias M. Hagos"