Given a cyclic quadrilateral
, let the diagonals
and
meet at
and the lines
and
meet at
. The midpoints of
and
are
and
, respectively. Show that
is tangent at
to the circle through the points
,
and
.
Proposed by David Monk, United Kingdom
%V0
Given a cyclic quadrilateral $ABCD$, let the diagonals $AC$ and $BD$ meet at $E$ and the lines $AD$ and $BC$ meet at $F$. The midpoints of $AB$ and $CD$ are $G$ and $H$, respectively. Show that $EF$ is tangent at $E$ to the circle through the points $E$, $G$ and $H$.
Proposed by David Monk, United Kingdom
Školjka