Given a rhombus with diagonals a and b, which contains an inscribed circle. The task is to find the area of that circle in terms of a and b.
Input: l = 5, b = 6 Output: 11.582 Input: l = 8, b = 10 Output: 30.6341
Approach: From the figure, we see, the radius of inscribed circle is also a height h=OH of the right triangle AOB. To find it, we use equations for triangle’s area :
Area AOB = 1/2 * (a/2) * (b/2) = ab/8 = 12ch
where c = AB i.e. a hypotenuse. So,
r = h = ab/4c = ab/4√(a^2/4 + b^2/4) = ab/2√(a^2+b^2)
and therefore area of the circle is
A = Π * r^2 = Π a^2 b^2 /4(a2 + b2)
Below is the implementation of above approach:
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