## TCS: P14

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• [Hatzipolakis - Lozada] Let ABC be a triangle and AhBhCh, AoBoCo the pedal triangles of H, O, (orthic,medial tr.) resp. Denote: Haa, Hbb, Hcc = the orthogonal
Message 1 of 1 , Aug 16, 2013

Let ABC be a triangle and AhBhCh, AoBoCo
the pedal triangles of H, O, (orthic,medial tr.) resp.

Denote:

Haa, Hbb, Hcc = the orthogonal projections of H
on OAo, OBo, OCo, resp.

Hab, Hac = the orhogonal projections of Haa
on OBo, OCo, resp.

Hbc, Hba = the orthogonal projections of Hbb
on OCo, OAo, resp.

Hca, Hcb = the orthogonal projections of Hcc
on OAo, OBo, resp.

1.1. HabHac, HbcHba, HcaHcb concur at a point H*

1.2. The Euler lines Ma,Mb,Mc of HaaHabHac, HbbHbcHba,
HccHcaHcb, resp. concur at H*

Perspector:

H*=((b^2+c^2)*a^6-(3*(c^4+b^4))*a^4+(b^2+c^2)*(3*b^4+3*c^4-2*b^2*c^2)*a^2-(b^4+4*b^2*c^2+c^4)*(b^2-c^2)^2)*a : : (trilinears)

H*=complement of X(185)

Reference:
http://tech.groups.yahoo.com/group/Anopolis/message/835
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