Let
be a triangle and
an exterior point in the plane of the triangle. Suppose the lines
,
,
meet the sides
,
,
(or extensions thereof) in
,
,
, respectively. Suppose further that the areas of triangles
,
,
are all equal. Prove that each of these areas is equal to the area of triangle
itself.
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Let $ABC$ be a triangle and $P$ an exterior point in the plane of the triangle. Suppose the lines $AP$, $BP$, $CP$ meet the sides $BC$, $CA$, $AB$ (or extensions thereof) in $D$, $E$, $F$, respectively. Suppose further that the areas of triangles $PBD$, $PCE$, $PAF$ are all equal. Prove that each of these areas is equal to the area of triangle $ABC$ itself.
Školjka