Given a semicircle with radius r, we have to find the largest square that can be inscribed in the semicircle, with base lying on the diameter.
Input: r = 5 Output: 20 Input: r = 8 Output: 51.2
Approach: Let r be the radius of the semicircle & a be the side length of the square.
From the figure we can see that, centre of the circle is also the midpoint of the base of the square.So in the right angled triangle AOB, from Pythagorus Theorem:
a^2 + (a/2)^2 = r^2
5*(a^2/4) = r^2
a^2 = 4*(r^2/5) i.e. area of the square
Below is the implementation of the above approach:
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