[alogo] Orthocenter projections

The projections {H1, H2} of the orthocenter H on the two bisectors at A of triangle ABC are on the line joining the middle E of BC with the center D of the Euler circle.

[0_0] [0_1]
[1_0] [1_1]

The middle H0 of AH and the middle E of BC define a diameter of the Euler circle parallel to OA, O being the circumcenter. Thus triangles AH0H1, H1EF, H0AH2 are isosceli etc....

By the way, note that (i) HH1AH2 is similar to AFA''A', (ii) Triangle H2EA' is isosceles, (iii) Angle HAF = angle(DEA')/2 = (B-C)/2. (iv) Triangles AH0H1, H1EF, AOF are similar isosceli.

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