be the circumcircle of triangle 
,
be the second intersection of 
and 
be a transversal of 
be intersections of 
with 
be a tangent line of 
is cyclic
be positive integers that satisfy the inequality![\[
\frac{a}{b} < \frac{x}{y} < \frac{c}{d}
\]](http://latex.artofproblemsolving.com/8/d/9/8d982d52e655546ac29039fa6e440e68821bfe7f.png)
with 
.
,
.
Y by Adventure10, Mango247, and 1 other user
Given a rhombus 
. A point 
is chosen on its side 
. The lines, which pass through and are perpendicular to 
and 
, meet line 
in points 
and 
respectively. Suppose that the lines 
have a common point. Find all possible values of a ratio 
.
S. Berlov, F. Petrov, A. Akopyan
. A point 
is chosen on its side 
. The lines, which pass through and are perpendicular to 
and 
, meet line 
in points 
and 
respectively. Suppose that the lines 
have a common point. Find all possible values of a ratio 
.S. Berlov, F. Petrov, A. Akopyan
concur in 
.
.
is a paralleologram so 
.
,
.
with 
.
and 
;
we have 
