Conceptual Geometry
Through a point inside a triangle three lines parallel to the triangle’s sides are drawn.
Denote the areas of the parts into which these lines divide the triangle as plotted in the figure.
Find the least value of .
The answer is 1.5.
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1 solution
The inside point must be the barycenter by doing so the ratio we get nine equal area triangles. Therefore ratio between the yellow triangles and its opposite blue diamond is 1/2, adding up we get 3/2.