Given a triangle $ABC$ and a point $X$, is it possible to only use Ruler and Compass, to draw a line $l$ through $X$, such that $l$ will split $ABC$ to two parts with equal area?
Ruler-and-Compass metric: draw a line from any point to separate the area of a triangle?
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geometric-construction
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0Can $X$ be anywhere in the plane of the triangle, or must $X$ lie within $ABC$? – 2017-01-16
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0@EdwardPorcella anywhere... – 2017-01-16
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0I think a median does the job and unless x lies on it, perhaps. – 2017-06-11