1978. Symmedian Points On Euler Line

1977. Triangles With Same Centroid

1976. A Locus For K005-Napoleon-Feuerbach Cubic

1975. Isogonal Inscribed Triangles

 

1974. Concurrency Points On Euler Line

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

1972. Collinear Points Related To K001-Neuberg Cubic

1971. Collinear Points On K001-Neuberg Cubic of ABC

1970. Lines Through Incenter

1969.Conics Intersecting Cubic Curves At a Fixed Point

 Let P be a triangle center on K001-Neuberg Cubic of ABC.

Any line through P intersect the  K001-Neuberg Cubic at P1 and P2.

*As P1, P2 varies on K001-Neuberg Cubic, the conic {A,B,C,P1,P2} intersect the K001-Neuberg Cubic at a fixed point.

**If P=X(1)-Incenter of ABC, fixed point is X(7164).

    If P=X(3)-Circumcenter of ABC, fixed point is X(1138).

    If P=X(4)-Orthocenter of ABC, fixed point is X(8431).

    If P=X(13)-1st Fermat-Toricelli point of ABC, fixed point is X(8445).

    If P=X(399) of ABC, fixed point is X(4).  

1968. Concyclic Points

1967. Concyclic Points

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

1965. A Type Of Circlecevian and Concyclic Points

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).

1963. A Triangle Inscribed In Nine-Point Circle

 Let A1B1C1 median triangle of ABC.

A2: Inverse of X(3)-Circumcenter of ABC in the circle with diameter B1C1. 
Define B2, C2 cyclically.

*A2B2C2 is inscribed in the Nine-Point Circle of ABC.

1962. A Type of Bicevian Conic

1961. Similar Triangles

1960. Triangles Inscribed In a Conic of ABC

1959. Circumcenter On Euler Line

1958. A Circumcenter On Euler Line of ABC

1957. Concurrent Circles On Circumcircle

1956. An Equilateral Triangle

 

1955. A Construction For the Perspector Of 2nd Lemoine Circle

Let K=X(6)-Symmedian point of ABC. Antiparallel from K to BC intersect the AB, AC at Ac, Ab resp.

Define Ba, Bc, Ca, Cb cyclically.

KA: Antipode of K respect to circle (KBaCa). Define KB, KC cyclically.

* ABC and KAKB,KC  are perspective triangles. Perspector is X(3527) = ISOGONAL CONJUGATE OF X(631)=perspector of 2nd Lemoine circle

1954. A Point On Median

1953. Concurrent Circles

1952. Concyclic Points

1951. Another Circle Centered At Incenter

1950. A Circle Centered At Incenter

1949. On Fermat's Configuration

1948. Gergonne-Nagel Conic

1947. A Conic Problem

1946. A-Mixtilinear Hyperbola

1945. Conics Related To Euler Line

1944. Collinear Points

1943. Four Congruent Circles

1942. Right Triangles Inscribed In Feuerbach Hyperbola

1941. A Property Of Orthocentroidal Circle

1940. Equal Area

1939. A Locus For K007-Lucas Cubic

1938. Collinear Points

1937. Concurrent Tangents

1936. An Equilateral Triangle

1935. Collinear Points

1934.A Property Of Jerabek Hyperbola

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

1929. A Locus For K004-Darboux Cubic