Given here is a right angle triangle with height l, base b & hypotenuse h, which inscribes a square which in turn inscribes a reuleaux triangle. The task is to find the maximum possible area of this reuleaux triangle.
Input: l = 5, b = 12, h = 13 Output: 8.77914 Input: l = 3, b = 4, h = 5 Output: 2.07116
Approach: We know, the side of the square inscribed within a right angled triangle is, a = (l*b)/(l+b), please refer Area of a largest square fit in a right angle triangle.
Also, in the reuleaux triangle, x = a.
So, x = (l*b)/(l+b).
So, Area of the Reuleaux Triangle is, A = 0.70477*x^2 = 0.70477*((l*b)/(l+b))^2.
Below is the implementation of the above approach:
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