Let
be a convex quadrilateral with non-parallel sides
and
. Assume that there is a point
on the side
such that the quadrilaterals
and
are circumscribed. Prove that there is a point
on the side
such that the quadrilaterals
and
are circumscribed if and only if
is parallel to
.
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Let $ABCD$ be a convex quadrilateral with non-parallel sides $BC$ and $AD$. Assume that there is a point $E$ on the side $BC$ such that the quadrilaterals $ABED$ and $AECD$ are circumscribed. Prove that there is a point $F$ on the side $AD$ such that the quadrilaterals $ABCF$ and $BCDF$ are circumscribed if and only if $AB$ is parallel to $CD$.
Školjka