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.
(In reply to
q. and possible soln by Steven Lord)
Yes that is a typo, the segments are (AF, BG, CH, DE) as you note. There are two pairs of parallel segments inside the square.
As for the circles inscribed in the trapezoids, I mean the circles touch each of the four sides. That makes the solution unique.
Doesn't the term "inscribed" mean that? Wikipedia to the rescue:
Not every polygon with more than three sides has an inscribed circle; those polygons that do are called tangential polygons.
If the trapezoids are tangential, find AE/AB.
|
|
Posted by Jer
on 2019-08-28 21:17:17 |
re: q. and possible soln - corrections and clarifications
