1995 IMO Problems
Problems of the 1995 IMO.
Contents
[hide]Day I
Problem 1
Let be four distinct points on a line, in that order. The circles with diameters
and
intersect at
and
. The line
meets
at
. Let
be a point on the line
other than
. The line
intersects the circle with diameter
at
and
, and the line
intersects the circle with diameter
at
and
. Prove that the lines
are concurrent.
Problem 2
Let be positive real numbers such that
. Prove that
Problem 3
Determine all integers for which there exist
points
in the plane, no three collinear, and real numbers
such that for
, the area of
is
.
Day II
Problem 4
The positive real numbers satisfy the relations
and
for
Find the maximum value that can have.
Problem 5
Let be a convex hexagon with
and
, such that
. Suppose
and
are points in the interior of the hexagon such that
. Prove that
.
Problem 6
Let be an odd prime number. How many
-element subsets
of
are there, the sum of whose elements is divisible by
?
See Also
1995 IMO (Problems) • Resources | ||
Preceded by 1994 IMO |
1 • 2 • 3 • 4 • 5 • 6 | Followed by 1996 IMO |
All IMO Problems and Solutions |