Q.219. Geometry.

Question 219.
Find distance x in terms of areas A, B, C in the following figure.

Answer 219.

A, B and C are the areas of parts A, B and C.

Let the area of the circular sector outside the square = m
=> B = A - (1/2) (2Rx - m)
and C = A - (2Rx - m) + x^2

=> C - 2B = x^2 - A
=> A + C - 2B = x^2
=> x = √(A + C - 2B).

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