of each imon 
become entangled if and only if the original imons 
are entangled, and each copy 
members from party 
,
members from party 
,
members from party 
,
members from party 
,
or more people involved).
that if they were to be considered the number of members from the four parties, it is possible that, after some time, all of the kidnapped people belong to the same party, under the same rules imposed by the wizard.
at 
meets sides 
and 
and 
be the circumcentre of 
is perpendicular to 
.
Y by HWenslawski
Let 
be a triangle and let 
and 
be the points where the incircle of is tangent to sides 
, 
, and 
, respectively. We call 
and 
the points diametrically opposite to and respectively, wrt the incircle of . Let us denote by 
and 
the intersection points of the lines 
with 
, the lines 
with 
and lines 
with 
respectively. Show that the lines 
, 
and 
are concurrent.
be a triangle and let 
and 
be the points where the incircle of is tangent to sides 
, 
, and 
, respectively. We call 
and 
the points diametrically opposite to and respectively, wrt the incircle of . Let us denote by 
and 
the intersection points of the lines 
with 
, the lines 
with 
and lines 
with 
respectively. Show that the lines 
, 
and 
are concurrent.
