1993. A Circle Centered At X(381)

1990. Concurrent Circles

1989. A Circle Centered at X(5476)

1983. A Circumcircle Through Circumcenter of ABC

1981. Euler To Euler

 

1980. Triangles Sharing The Same Centroid

1977. Triangles With Same Centroid

1976. A Locus For K005-Napoleon-Feuerbach Cubic

1966. A Lemoine Type Circle Centered At X(17508)

1952. Concyclic Points

1930. Remarks On A General Conic

1918. Myakishev Associate Triangles

1917. Myakishev Associate Triangles

1916. Centroids On Euler Line

1898. Collinear Points

1896. Collinear Points

1889. Symmedian Points On Euler Line

1883. A Symmedian point On Euler Line

1875. Same Centers

 1. ) Let  and  be the orthocenter and Nagel's point of . Let  be the projections of  on .

*  and  have same incenter.

2.) Let  be the symmedian point of . Let  be the projections of  on perpendicular bisectors of 
**  and  have same centroid.

1866. A Property Of Kiepert Circum Hyperbola

 This problem is inspired from #5175 by Tran Quang Hung.

Let P,Q be two points on Kiepert hyperbola of ABC. Circles APQ, BPQ, CPQ intersects the Kiepert hyperbola of ABC at A', B',C' resp.
R=X(2)-Centroid of of A'B'C' lies on Kiepert hyperbola of ABC.
So we have a transformation T, T(P,Q)->R, Let's show it with * operation. Then we have:
P*Q=R, P*R=Q, Q*R=P