2016 JBMO Problems

Revision as of 00:42, 23 April 2018 by Leonariso (talk | contribs) (Problem 2)

Problem 1

A trapezoid $ABCD$ ($AB || CF$,$AB > CD$) is circumscribed.The incircle of the triangle $ABC$ touches the lines $AB$ and $AC$ at the points $M$ and $N$,respectively.Prove that the incenter of the trapezoid $ABCD$ lies on the line $MN$.

Solution

Problem 2

Let $a,b,c$be positive real numbers.Prove that

$\frac{8}{(a+b)^2 + 4abc} + \frac{8}{(b+c)^2 + 4abc} + \frac{8}{(a+c)^2 + 4abc} + a^2 + b^2 + c ^2 \ge \frac{8}{a+3} + \frac{8}{b+3} + \frac{8}{c+3}$.

Solution

Problem 3

Solution

Problem 4

Solution

See also

2016 JBMO (ProblemsResources)
Preceded by
2015 JBMO Problems
Followed by
2017 JBMO Problems
1 2 3 4
All JBMO Problems and Solutions


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