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An art gallery engages a security guard to ensure that the items displayed are protected. The diagram below represents the plan of the gallery where the boundary walls are opaque. The location the security guard posted is identified such that all the inner space (shaded region in the plan) of the gallery is within the line of sight of the security guard.

If the security guard does not move around the posted location and has a $360^{\circ}$ view, which one of the following correctly represents the set of $\text{ALL}$ possible locations among the locations $\text{P, Q, R}$ and $\text{S},$ where the security guard can be posted to watch over the entire inner space of the gallery.

  1. $\text{P}$ and $\text{Q}$
  2. $\text{Q}$
  3. $\text{Q}$ and $\text{S}$
  4. $\text{R}$ and $\text{S}$
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Given that,  the plan of the gallery where the boundary walls are ${\color{Purple}{\text{opaque}}}$ (not able to be seen through; not transparent).

If the security guard will be posted on ${\color{Red}{\text{‘P’}}}$ then he/she can’t watch the visibility side of ${\color{Magenta}{\text{‘R’}}}$ and vice versa. But if the security guard will be posted at ${\color{Blue}{\text{‘Q’}}}$ and ${\color{Green}{\text{‘S’}}}$ then the security guard can watch over the entire inner space of the gallery.

Correct Answer $:\text{C}$

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