Feynman Triangle Variation

For a triangle ABC in the plane, if each side is divided by a point (1/p), (p >= 2) (measured say anti-clockwise), find a formula relating the area of ABC with that of A'B'C' (triangle formed by these points).

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Feynman Triangle Variation: 1/3 division

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Feynman Triangle Variation: 1/4 division

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Feynman Triangle Variation: 1/5 division

Can you generalize even further for sides divided into different ratios?


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Michael de Villiers, Sept 2009.