Difference between revisions of "2016 JBMO Problems"
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==Problem 2== | ==Problem 2== | ||
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| + | Let <math>a,b,c </math>be positive real numbers.Prove that | ||
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| + | <math>\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}</math>. | ||
[[2016 JBMO Problems/Problem 2#Solution|Solution]] | [[2016 JBMO Problems/Problem 2#Solution|Solution]] | ||
Revision as of 00:42, 23 April 2018
Problem 1
A trapezoid 
(
,
) is circumscribed.The incircle of the triangle 
touches the lines 
and 
at the points 
and 
,respectively.Prove that the incenter of the trapezoid lies on the line 
.
Problem 2
Let 
be positive real numbers.Prove that
.
Problem 3
Problem 4
See also
| 2016 JBMO (Problems • Resources) | ||
| Preceded by 2015 JBMO Problems |
Followed by 2017 JBMO Problems | |
| 1 • 2 • 3 • 4 | ||
| All JBMO Problems and Solutions | ||
