Saturday, July 11, 2015

481: Two Circles and One Square

What is the red area?
The two vertices of the square are the centers of two tangent and congruent circles. If the length of a side is 8√2, what is the area of the red part peeping out?

Here is the real question: Does it matter if the circles are congruent, as long as they're tangent and the centers are at the vertices of the square?


  1. Nice extension, great diagram (Geogebra!) and thanks for the mention! While the area of the square would be constant, (R+r)²/2, the sum of the areas of the quarter-circles would involve the factor R²+r² which isn't constant. Am I missing something?

  2. Not missing anything. Those parentheses matter.