1995 IMO Problems
Problems of the 1995 IMO.
Contents
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 |