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4 RH points (updated)

R - circumcenter of ABC. H - orthocenter of ABC. RH1 point is constructed as defined here: https://math.stackexchange.com/questions/3769174/point-lying-on-jerabek-hyperbola AX1,BY1,CZ1 intersect at the point RH1. GU,EF intersect at X1. GU,WV intersect at Y1. WV,EF intersect at Z1. Then, similarly: AX2, BY2, CZ2 intersect at RH2. (FW,UV intersect at X2. UV,GE intersect at Y2. FW,EG intersect at Z2) AX3, BY3, CZ3 intersect at RH3. (UW,FG intersect at X3. FG,EV intersect at Y3. UW,EV intersect at Z3) AX4, BY4, CZ4 intersect at RH4. (VF,UE intersect at X4. GW,VF intersect at Y4. GW,UE intersect at Z4) RH(1), RH(2), RH(3) lie on Jerabek hyperbola that goes through R,H,A,B,C. as it has been kindly proved by mathstackexchange member Blue: https://math.stackexchange.com/a/3748904/409 K4 is the intersection point of A_RH3, B_RH2, C_RH1 K3 is the intersection point of A_RH4, B_RH1, C_RH2 K2 is the intersection point of A_RH1, B_RH4, C_RH3 K1 is the intersection point of A_RH2, B_RH3, C_RH4 Then, K1,K2, K3, R, H are collinear. (belong to Euler line) X1, X2, Y1, Y3, Z2, Z3 belong to a conic. X1, X2, Y2, Y4, Z1, Z4 belong to a conic. (shown as ellipse here) X3, X4, Y1, Y3, Z1, Z4 belong to a conic. X3, X4, Y2, Y4, Z2, Z3 belong to a conic. (1,2) (1,3) (2,3) 1,2,3 (1,2) (2,4) (1,4) 1,2,4 (3,4) (1,3) (1,4) 1,3,4 (3,4) (2,4) (2,3) 2,3,4 All 4 conics can be seen here : https://www.geogebra.org/geometry/w3vv6p5q This configuration apparently has a plethora of remarkable properties. and I wonder how many of those have been already proven/ or properly catalogued. For instance, Lines RH1_K1, RH2_K2, RH3_K3, RH4_K4 intersect at some point S...