Geometry · Midlines · Area bisection · Parallelograms · Dissection
Problem 5, 2008
A triangle \(ABC\) has \(AB = 2\), \(BC = 3\) and \(CA = 4\). Find a polygonal line \(XYZ\) whose endpoints \(X\) and \(Z\) lie on the boundary of the triangle \(ABC\), such that
\[ XY = YZ = 1 \]
and such that the line \(XYZ\) divides the triangle \(ABC\) into two parts of equal area.
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Serbian Regional Competition 2008, high school grade I, category A, problem 5. Organized by the Mathematical Society of Serbia (DMS). Source