1829. Constructions For X(14790) and X(18569)

 1. Let O=X(3) circumcenter of ABC. Ha, Hb, Hc orthocenters of OBC, OCA, OAB resp.

La=Antiparallel from Ha to BC. Define Lb, Lc cyclically.
Let A1B1C1 triangle bounded by lines La,Lb,Lc.
* Orthocenter of A1B1C1 lies on Euler line of ABC. Its X(14790)= Conjugate-Couple of X(22) In the Range In Involution {X(2),X(5)}, {X(3),X(4)}.

2.Let H=X(4) orthocenter of ABC. Oa, Ob, Oc circumcenters of HBC, HCA, HAB resp.
La=Antiparallel from Oa to BC. Define Lb, Lc cyclically.
Let A1B1C1 triangle bounded by lines La,Lb,Lc.
* Circumcenter of A1B1C1 lies on Euler line of ABC. Its X(18569)= Ehrmann-Side-Ehrmann-Vertex Similarity Image of X(382).