1997 JBMO Problems
Problem 1
Show that given any 9 points inside a square of side length 1 we can always find 3 that form a triangle with area less than .
Problem 2
Let . Compute the following expression in terms of :
Problem 3
Let be a triangle and let be the incenter. Let , be the midpoints of the sides and respectively. The lines and meet at and respectively. Prove that .
Problem 4
Determine the triangle with sides and circumradius for which .
Problem 5
Let , , , be positive integers such that Show that at least two of the numbers are even.
See also
1997 JBMO (Problems • Resources) | ||
Preceded by First Olympiad |
Followed by 1998 JBMO Problems | |
1 • 2 • 3 • 4 • 5 | ||
All JBMO Problems and Solutions |