A triangle of maximal area#2024
On the plane, you are given a circle of radius . From it, cut out two circles of radii R_1 and R_2 such that R_1 + R_2 = R. Find the maximum area of a triangle that can fit into the resulting figure.
The input data contain a variety of test cases (no more than ). Each test case is given in a separate row with two numbers R_1 and R_2 (1 \leq R_1, R_2 \leq 10^6)—the radii of the circles. The numbers are separated by a space. Input ends with EOF.
For each pair of radii from the input, output on a separate line the maximum area of the inscribed triangle, with an absolute or relative error not exceeding 10^{-8}.
Example 1