26 May 2020

Another geometry puzzle

I sent this to my nephews since they have been sending me a few puzzles. See if you can beat them to it…

Orange circle inscribed inside an equilateral triangle inscribed inside a larger circle. Can you prove that the orange area is the same as the addition of the two purple areas?

Posted May 26, 2020 by Rajib Roy in category "Puzzles


  1. By Somnath D on

    Rajibda consider the large circle area as 3x+3y+z, where each variable represents each unique shape. Z is the area of small circle. Now, the radius of big circle is 2 times that of small circle, as the centroid is located at 2/3 the distance from the vortex. Therefore area ratio between big and small circle is 4. Therefore 3x+3y+z = 4z. From this, x+y=z. The two purple areas add up to the orange area.

  2. By Rajib Roy (Post author) on

    I am debating whether to accept the premise the centroid is located at 2/3 distance. It is a true statement though. I am inclined to accept that as something as “given” without having to prove.

    On the other hand, there is another way of proving why the larger circle will be 4 times the smaller circle. Want to give it another shot?


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