ABCD with center O and A'B'C'D' with center O' are congruent squares with O on A'D' and O' on AD.
If OO' is small enough then the squares' overlap will be a hexagon. Let E be the intersection of CD and C'D'. In the case that triangle OEO' is equilateral, find the area of the overlap.
If OO' is large enough then the square's overlap will be a quadrilateral. Let F be the intersection of AD and A'D'. In the case that triangle OFO' is equilateral, find the area of the overlap.
This problem has two parts. I have solved the second part, and I will post the solution when I am done with the first part.
I have an issue with the first part. I find that if I label the vertices of the two squares ABCD, A'B'C'D', running consistently (e.g, both CW), CD and C'D' will not intersect. But, if I change the rules a little, things can work:
If I label the vertices inconsistently, with one set running CW and the other running CCW, then the conditions may be met.
Alternatively, I can place O' on AD, and place O on B'C'.
Either change allows for the situation described: a short OO', a hexagonal overlap, and an equilateral triangle OEO', with E on the intersection of CD and C'D'.
Edited on March 26, 2022, 10:23 pm
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