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How to find the area of green region in terms of yellow, blue and red region in the following figure?

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The triangle is any random triangle and an arbitrary point $P$ is taken where all the colored regions coincide.

The answer given is $$G = \frac{BY(Y + B + 2R)}{R^2 - BY}$$

But I'm not able to find out. Please help.

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    All I know is that had the triangle been equilateral, then the sum of perpendiculars from $P$ to the different sides would have been same as the altitude of the triangle.2012-07-15
  • 3
    If you can prove it for a unit right triangle, then it would hold in general, since all triangles are affine transformations of a unit right triangle, and affine maps preserve relative areas.2012-07-15

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