View source for Trigonometry/Circles and Triangles/Area bisectors

'''Area bisectors'''

As already noted, the three medians of a triangle each bisect its area.  So do the lines parallel to each side of the triangle dividing the other two sides in the ratio <math>\sqrt 2+1:1</math>.  These six lines form four concurrent triplets: the three medians and each median with the lines parallel with the two sides not cut by the median.  The latter three triplets define a triangle of which the medians are the same as those of the original triangle.


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