geometry problems from Leningrad Math Olympiads (LMO)
with aops links in the names
with aops links in the names
named as Saint Petersburg from 1992
(continued here)
(continued here)
1935- 1992
under construction
1935 Leningrad MO P
1935 Leningrad MO P
1936 Leningrad MO P
1936 Leningrad MO P
1937 Leningrad MO P
1937 Leningrad MO P
1938 Leningrad MO P
1938 Leningrad MO P
1939 Leningrad MO P
1939 Leningrad MO P
1940 Leningrad MO P
1940 Leningrad MO P
1941 Leningrad MO P
1941 Leningrad MO P
1945 Leningrad MO P
1945 Leningrad MO P
1946 Leningrad MO P
1946 Leningrad MO P
1947 Leningrad MO P
1947 Leningrad MO P
1948 Leningrad MO P
1948 Leningrad MO P
1949 Leningrad MO P
1949 Leningrad MO P
1950 Leningrad MO P
1950 Leningrad MO P
1951 Leningrad MO P
1951 Leningrad MO P
1952 Leningrad MO P
1952 Leningrad MO P
1953 Leningrad MO P
1953 Leningrad MO P
1954 Leningrad MO P
1954 Leningrad MO P
1955 Leningrad MO P
1955 Leningrad MO P
1956 Leningrad MO P
1956 Leningrad MO P
1957 Leningrad MO P
1957 Leningrad MO P
1958 Leningrad MO P
1958 Leningrad MO P
1959 Leningrad MO P
1959 Leningrad MO P
1960 Leningrad MO P
1960 Leningrad MO P
1961 Leningrad MO P
1961 Leningrad MO P
1962 Leningrad MO P
1963 Leningrad MO P
1963 Leningrad MO P
1964 Leningrad MO P
1964 Leningrad MO P
1965 Leningrad MO P
1965 Leningrad MO P
1966 Leningrad MO P
1966 Leningrad MO P
1967 Leningrad MO P
1967 Leningrad MO P
1968 Leningrad MO P
1968 Leningrad MO P
1969 Leningrad MO P
1969 Leningrad MO P
1970 Leningrad MO P
1970 Leningrad MO P
1971 Leningrad MO P
1971 Leningrad MO P
1972 Leningrad MO P
1972 Leningrad MO P
1973 Leningrad MO P
1973 Leningrad MO P
Three vertexes of a square are given. Each step, we can add symmetry of a point from another point to our collection. Is it possible to add that square's fourth point to our collection?
Three vertexes of a square are given. Each step, we can add symmetry of a point from another point to our collection. Is it possible to add that square's fourth point to our collection?
1974 Leningrad MO P
1974 Leningrad MO P
1975 Leningrad MO P
1975 Leningrad MO P
1976 Leningrad MO P
1976 Leningrad MO P
1977 Leningrad MO P
1977 Leningrad MO P
1978 Leningrad MO P
1978 Leningrad MO P
1979 Leningrad MO P
1979 Leningrad MO P
1980 Leningrad MO P
1980 Leningrad MO P
1981 Leningrad MO P
1981 Leningrad MO P
1982 Leningrad MO P
1982 Leningrad MO P
1983 Leningrad MO P
1983 Leningrad MO P
1984 Leningrad MO P
1984 Leningrad MO P
1985 Leningrad MO P
1985 Leningrad MO P
1986 Leningrad MO P
1986 Leningrad MO P
1987 Leningrad MO P
1987 Leningrad MO P
Altitude $CH$ and median $BK$ are drawn in an acute triangle $ABC,$ and it is known that $BK=CH$and $\angle KBC= \angle HCB.$ Prove that triangle $ABC$ is equilateral.
Altitude $CH$ and median $BK$ are drawn in an acute triangle $ABC,$ and it is known that $BK=CH$and $\angle KBC= \angle HCB.$ Prove that triangle $ABC$ is equilateral.
1988 Leningrad MO P
1988 Leningrad MO P
1989 Leningrad MO P
1989 Leningrad MO P
1990 Leningrad MO P
1990 Leningrad MO P
1991 Leningrad MO P
1991 Leningrad MO P
Unknown year yet:
19xx Leningrad MO P
Let $ABCD$ be a convex quadrilateral with a point $O$ in the interior and points $P,Q,R,S$ on the sides $AB,BC,CD,DA$ respectively such that $APOS\text{ and }CROQ$ are parallelograms. Prove that \[\sqrt{S_{BQOP}}+\sqrt{S_{DSOR}}\le \sqrt{S_{ABCD}}.\]
Unknown year yet:
19xx Leningrad MO P
Let $ABCD$ be a convex quadrilateral with a point $O$ in the interior and points $P,Q,R,S$ on the sides $AB,BC,CD,DA$ respectively such that $APOS\text{ and }CROQ$ are parallelograms. Prove that \[\sqrt{S_{BQOP}}+\sqrt{S_{DSOR}}\le \sqrt{S_{ABCD}}.\]
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