and 
. Prove that
where 
is a perfect cube
such that 
and exist 
odd numbers 
satisfied all conditions below:![$\sqrt[k]{a_1}+\sqrt[k]{a_2} + ... + \sqrt[k]{a_n} = \sqrt[k]{b_1}+\sqrt[k]{b_2} + ... + \sqrt[k]{b_m} $](http://latex.artofproblemsolving.com/c/9/e/c9e051a562376b2b9e02e82d46a41126874cdf60.png)
for all positive number 
Y by Mango247
Circle 
of unit radius passes through the vertices 
and 
of triangle 
and intersects its sides 
and 
for the second time at points 
and 
, respectively. Points 
and 
are marked on rays 
and 
, respectively, such that 
and 
= . Find the distance between the centers of the circumscribed circles of triangles 
and 
.
of unit radius passes through the vertices 
and 
of triangle 
and intersects its sides 
and 
for the second time at points 
and 
, respectively. Points 
and 
are marked on rays 
and 
, respectively, such that 
and 
= . Find the distance between the centers of the circumscribed circles of triangles 
and 
.This post has been edited 1 time. Last edited by parmenides51, Feb 22, 2021, 12:04 AM
