1997 JBMO Problems
Problem 1
(Bulgaria) 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
(Cyprus) Let . Compute the following expression in terms of
:
Problem 3
(Greece) 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
(Romania) 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 |