## 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.