Given square ABCD with E on AB, F on BC, G on CD, H on DA, AE=BF=CG=DH. Segments AF, BG, CH, CE dissect the square into 4 triangles, 4 trapezoids and a central square.
If circles can be inscribed in the trapezoids which have the same radius as the inscribed circle of the central square, find AE/AB.
I suspect the problem, as posed, has a typo. The list of segments: (AF, BG, CH, CE), would seem more natural and symmetric if chosen as: (AF, BG, CH, DE). Otherwise, I can not find the claimed dissection. Maybe I'm wrong, but the problem's listed difficulty (as easy) makes me think I may be right.
Assuming the latter list is correct, I can see possible configurations as shown
here.
I have shown two examples where AE/AB have very different values, with the constraints met, and so I think the ratio asked for, instead of being single-valued, has a range.
I am sorry if I have misinterpreted the problem, but if I get it,
there is not single ratio for AE/AB.
Edited on August 28, 2019, 4:23 pm
q. and possible soln
