Problem 61088. Covering a four-pointed star polygon by circles

Given the area, A, of a star polygon formed by the rectangle, with dimensions L×2L, and four triangles, with height h from their bases to the vertices, consider the circles that cover the distances between opposite vertices (cf. figure below).
Given (A,h), return the 2x2 matrix M = [A1/π a1; A2/π a2], where
  • in the first row (i=1), A1 stands for the area of the circle that covers the minimum distance (cf. left figure), and a1 stands for the logical 1 if A1 is smaller than or reaches the area A or a1 stands for the logical 0 if A1 surpasses A;
  • in the second row (i=2), A2 stands for the area of the circle that covers the maximum distance (cf. right figure), and a2 has the same previous false-true meaning relative to the areas A2 and A. Obviously, that A2 > A holds true, then a2 = 0.
input: (A, h)
output: M = [A1/π a1; A2/π 0]
Covering by circles
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100.0% Correct | 0.0% Incorrect
Last Solution submitted on Dec 03, 2025

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