2001 JBMO Problems
Problem 1
Solve the equation in positive integers.
Problem 2
Let be a triangle with and . Let be an altitude and be an interior angle bisector. Show that for on the line we have . Also show that for on the line we have .
Problem 3
Let be an equilateral triangle and on the sides and respectively. If (with ) are the interior angle bisectors of the angles of the triangle , prove that the sum of the areas of the triangles and is at most equal with the area of the triangle . When does the equality hold?
Bonus Question:
In the above problem, prove that .
- Proposed by Kris17
Problem 4
Let be a convex polygon with 1415 vertices and perimeter 2001. Prove that we can find 3 vertices of which form a triangle of area smaller than 1.
See Also
2001 JBMO (Problems • Resources) | ||
Preceded by 2000 JBMO |
Followed by 2002 JBMO | |
1 • 2 • 3 • 4 | ||
All JBMO Problems and Solutions |