and 
.
and 
.
Equality holds when 
or 
be a cyclic quadrilateral whose opposite sides are not parallel. Suppose points 
lie in the interiors of segments 
respectively, such that 
Let 
intersect 
at 
,
intersect 
at 
.
and 
.
Where 
Y by
Given a circle and a straight line 
passing through its center (points 
and 
are fixed, is outside the circle, and is inside). Find the locus of the intersection of lines 
and 
, where 
is an arbitrary diameter of the circle.
(A. Akopyan, A. Zaslavsky)
passing through its center (points 
and 
are fixed, is outside the circle, and is inside). Find the locus of the intersection of lines 
and 
, where 
is an arbitrary diameter of the circle.(A. Akopyan, A. Zaslavsky)
and radius 
.
with 
and 
.
,
.
.
is the circle ![$[x(a+b)-2ab]^{2}+[y(a+b)]^{2}=r^{2}(a-b)^{2}$](http://latex.artofproblemsolving.com/6/1/9/619ed3cd7a44f65780fab2b9ef9c9982b91a169a.png)
.
