The One-Seventh Area Triangle
The one-seventh area triangle is a special figure that can be constructed within any given triangle, using the following steps:
Draw three cevian lines, each connecting one vertex of the triangle to a point which is one-third of the distance between the vertices of the opposite side.
Let the intersections of these three cevian lines form the vertices of a smaller triangle completely contained within the original figure. This inner triangle has an area equal to one-seventh the area of the given triangle.
In the plot below, click to add three points defining a triangle. Then, click "Add One-Seventh Area Triangle". To see an animated demonstration, click "Show Proof".
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