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In the figure alongside, $\triangle \text{ABC}$ is equilateral with area $\text{S. M}$ is the mid-point of $\text{BC and P}$ is a point on $\text{AM}$ extended such that $\text{MP = BM}$. If the semi-circle on $\text{AP intersects CB}$ extended at $\text{Q}$ and the area of a square with $\text{MQ}$ as a side is $\text{T}$, which of the following is true? 

  1. $\text{T} = \sqrt{2}\; \text{S}$
  2. $\text{T = S}$
  3. $T = \sqrt{3}\; \text{S}$
  4. $\text{T = 2S}$
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