and 
Prove that
it can draw the line which forms the interior angle bisector of 
.
in the plane . Prove that Euclid can use the splitter several times to draw the centre of circle passing through 
and 
.
,
satisfying 
,
?
and 
such that![\[
1^n + 2^n + 3^n + \cdots + n^n = x!
\]](http://latex.artofproblemsolving.com/6/4/b/64b5f5919fd3710cc15e96724918eae216c8e4f0.png)
Y by Adventure10
Let 
be a triangle having 
as lengths of its sides and let 
be another triangle having 
as lengths of its sides. If 
are the areas of the two triangles, prove that
![\[16PQ \leq a^2(-u^2 + v^2 + w^2) + b^2(u^2 - v^2 + w^2) + c^2(u^2 + v^2 - w^2).\]](//latex.artofproblemsolving.com/c/e/2/ce2e2158f5bab37a148a66177edb411bab905516.png)
When does equality hold?
be a triangle having 
as lengths of its sides and let 
be another triangle having 
as lengths of its sides. If 
are the areas of the two triangles, prove that![\[16PQ \leq a^2(-u^2 + v^2 + w^2) + b^2(u^2 - v^2 + w^2) + c^2(u^2 + v^2 - w^2).\]](http://latex.artofproblemsolving.com/c/e/2/ce2e2158f5bab37a148a66177edb411bab905516.png)
When does equality hold?
