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?
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Can $X$ be anywhere in the plane of the triangle, or must $X$ lie within $ABC$? – Edward Porcella Jan 16 '17 at 00:15
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@EdwardPorcella anywhere... – athos Jan 16 '17 at 00:24
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I think a median does the job and unless x lies on it, perhaps. – tighten Jun 11 '17 at 21:19