Let
be a cyclic quadrilateral. Let
and
be variable points on the sides
and
, respectively, such that
. Let
be the point on the segment
such that
. Prove that the ratio between the areas of triangles
and
does not depend on the choice of
and
.
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Let $ABCD$ be a cyclic quadrilateral. Let $E$ and $F$ be variable points on the sides $AB$ and $CD$, respectively, such that $AE:EB=CF:FD$. Let $P$ be the point on the segment $EF$ such that $PE:PF=AB:CD$. Prove that the ratio between the areas of triangles $APD$ and $BPC$ does not depend on the choice of $E$ and $F$.
Školjka