1991. Circumcenter On Euler Line

1988. Circumcenters On Euler Line

 Let ABC be a triangle with P, Q are two points on Euler line of ABC.

A',B',C' are inverse images of A,B,C through circle diameter PQ.

* Circumcenter of  A'B'C' lies on Euler line of ABC.

1987. Circumcenter On Euler Line

 Let H=X(4)-Orthocenter of ABC. A1B1C1 cevian triangle of H. B1A, C1A are reflections of B1, C1 on A.

LA, line through B1A, C1A. define LB, LC cyclically.

A2B2C2 triangle bounded by lines LA, LB, LC.

* Circumcenter of  A2B2C2 lies on Euler line of ABC.

1986. Circumcenters On Euler Line

1981. Euler To Euler

 

1974. Concurrency Points On Euler Line

1973. A Construction For X(10020) = 22nd HATZIPOLAKIS-MONTESDEOCA POINT

1964. A Construction For X(18569)

 Let A1B1C1 reflection triangle of X(3)-circumcenter on the side lines of ABC.

Tangents to circumcircle of A1B1C1 at A1, B1, C1 form a triangle A2B2C2.*

*Circumcenter of A2B2C2 lies on Euler line of ABC. It's X(18569).

1959. Circumcenter On Euler Line

1958. A Circumcenter On Euler Line of ABC

1945. Conics Related To Euler Line

1933. A Nine-Point Center On Euler Line

1932. An Orthocenter On Euler Line

1931. A Circumcenter On Euler Line

1930. Remarks On A General Conic

1924. Constant Ratios In Triangle

1920. A Line Perpendicular To Euler Line

1919. Collinear Kosnita Points

1916. Centroids On Euler Line

1914. Circumcenters On Euler Line