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Question
What is the area of a square inscribed in a circle of diameter p cm ?
Solution
The diameter of the circle = Diagonal of the square = p
We know that diagonal of a square = \[\sqrt{2}a\]
\[\Rightarrow \sqrt{2}a = p\]
\[ \Rightarrow a = \frac{p}{\sqrt{2}}\]
Thus, the area of the square = \[a^2 = \left( \frac{p}{\sqrt{2}} \right)^2 = \frac{p^2}{2} {cm}^2\]
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