What is the value of \frac{2(A_{1}+A_{2})}{A_{1}-3A_{2}} ?

Consider the following for the next two (02) items that follow : The circle x^{2}+y^{2}-2x=0 is partitioned by line y=x in two segments. Let A_{1}, A_{2} be the areas of major and minor segments respectively.

  1. A. \pi
  2. B. 1
  3. C. -1
  4. D. -\pi

Correct Answer: A. \pi

Explanation

The sum A_1 + A_2 is the total area of the circle, which is \pi. From the previous solution, A_1 = \frac{3\pi+2}{4} and A_2 = \frac{\pi-2}{4}. The denominator is A_1 - 3A_2 = \frac{3\pi+2}{4} - 3\left(\frac{\pi-2}{4}\right) = \frac{3\pi+2-3\pi+6}{4} = \frac{8}{4} = 2. Substituting these into the given expression yields \frac{2(\pi)}{2} = \pi.

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