Problem 57874. Easy Sequences 107: Minimized Circumcircle-Incircle Areas Ratio of Partial Pythagorean Triangles
We define a Partial Pythagorean Triangle (PPT) as a right triangle wherein the hypotenuse and at least one leg are integers. Thus, the triples and represent a PPT, while , and do not.
Given the limit P, find the area of the PPT with perimeter , such that the ratio of the areas of the triangle's circumcircle to its incircle, , is as small as possible.
Please present the answer rounded-off to the nearest integer.
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