Let $L_0,L_1,L_2,L_3,L_4$
be five lines in general position on the Euclidean
plane---think of the subscripts mod $5$ and draw $L_i$
as the consecutive lines
of a (not necessarily regular!) pentagram.
Let $C_i$ be the circle inscribed
about the triangle formed by $L_i$, $L_{i-2}$, and
$L_{i+2}$. Then $C_{i-1}$ and
$C_{i+1}$ meet at the intersection of
$L_{i-1}$ and $L_{i+1}$, and again at some
other point $P_i$ (which we take to be the same
point if the two circles are
tangent there). Show that these five points $P_i$ are concyclic.
.
Actually, it isn't open, but some years ago presented to me as open,
with computer-graphical evidence for it...
|
1 | [made Community Wiki] | ||
|
|
||||
