Construct line AB, and line CD perpendicular to it. Their intersection is R.
Construct circle O1, radius, 6 on R. U is a point on O1 in the first (positive) quadrant of AB/CD.
Construct circles O2, radius 11, and O3, radius 7, on U. These cross AB and CD at P and Q respectively.
Since each of the legs PR and QR has length √(X/Y), they are the same length. This occurs when PQ is near 17. That would give the answer X/Y= 289/2.
However, it seems that PQ may be slightly less than 17, and closer to 16.994, giving X/Y a value very close to 7599289/632403.
Alternatively, each of PR and QR could have a different length expressible as the square root of a rational fraction, but it seems that in that case multiple solutions are possible.
Edited on June 10, 2016, 2:06 am

Posted by broll
on 20160610 01:40:25 