,
,
with center 
and radius 
.
the midpoint of side 
intersects the circle 
.
be a point on the circle 
and 
.
.
such that for any real value of 
we have:
and 
are points, such that 
,
= 
and 
and 
passes through the fix point.
Consider an 
-
in the plane. An eligible set is a non-empty set of the form 
where 
determine the smallest possible number of eligible subsets 
Y by Adventure10, Mango247
Let 
is a tetrahedron. Denote by 
, 
the feet of the perpendiculars from 
and 
, respectively to the opposite faces. Show that 
and 
intersect if and only if 
is perpendicular to 
. Do they intersect if 
?
is a tetrahedron. Denote by 
, 
the feet of the perpendiculars from 
and 
, respectively to the opposite faces. Show that 
and 
intersect if and only if 
is perpendicular to 
. Do they intersect if 
?
, mostly 
geometry. I really was surprised.
