2012 JBMO Problems
Contents
[hide]Section 1
Let be positive real numbers such that . Prove that When does equality hold?
Section 2
Let the circles and intersect at two points and , and let be a common tangent of and that touches and at and respectively. If and , evaluate the angle .
Section 3
On a board there are nails, each two connected by a rope. Each rope is colored in one of given distinct colors. For each three distinct colors, there exist three nails connected with ropes of these three colors. a) Can be ? b) Can be ?
Section 4
Find all positive integers and such that .
See Also
2012 JBMO (Problems • Resources) | ||
Preceded by 2011 JBMO Problems |
Followed by 2013 JBMO Problems | |
1 • 2 • 3 • 4 | ||
All JBMO Problems and Solutions |