BrainDen.com - Brain Teasers

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Applying the Pythagorean theorem on the right triangle formed from the circle's center and the red square's right side,

1 = R/4 + R

where R is the area of the red square, gives us R = 4/5. The red triangle is a fourth of this: 1/5.

Applying the Pythagorean theorem for the right triangle formed from a corner of the black square and a segment of the circle's diameter,

1 = B/4 + B/4

where B is the area of the black square, gives us B = 2.

So the red triangle occupies a 10th of the black square.

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I had thought of making this a different problem: Given the black square (only) construct a shape inside the square that is 1/10 of its area.

It would entail making the circumcircle, the red square inscribed in the upper semicircle (the hard part) and finally the two red diagonals.

I wonder  if anyone would have gotten that solution or  if there is a simpler way.

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I had thought of making this a different problem: Given the black square (only) construct a shape inside the square that is 1/10 of its area.

It would entail making the circumcircle, the red square inscribed in the upper semicircle (the hard part) and finally the two red diagonals.

I wonder  if anyone would have gotten that solution or  if there is a simpler way.

I agree. That would have been a much harder problem.

I probably wouldn't have been able to solve it. I didn't realize this was an original puzzle. Good job!

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