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Home » The inradius $ r $ is given by $ r = - Deep Underground Poetry

The inradius $ r $ is given by $ r = - Deep Underground Poetry

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 The circumference of the circle is given by $ 2\pi R = 10\pi $, so solving for $ R $:

📌 R = 5 \text{ cm}

📌 Since the square is inscribed in the circle, the diagonal of the square equals the diameter of the circle:

📌 \text{Diagonal} = 2R = 10 \text{ cm}

📌 For a square with side $ s $, the diagonal is $ s\sqrt{2} $. Therefore:

📌 s\sqrt{2} = 10 \Rightarrow s = \frac{10}{\sqrt{2}} = 5\sqrt{2}

📌 The area of the square is:

📌 s^2 = (5\sqrt{2})^2 = 25 \cdot 2 = 50

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