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Home » The diameter of the circle is twice the radius: - Abbey Badges

The diameter of the circle is twice the radius: - Abbey Badges

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 \frac{A}{r^2} = \frac{A}{\left(\frac{A}{s}\right)^2} = \frac{A \cdot s^2}{A^2} = \frac{s^2}{A}

📌 Now express \(A\) and \(s\) in terms of \(c\). For a right triangle:

📌 A = \frac{1}{2}ab, \quad \text{and} \quad a^2 + b^2 = c^2

📌 Also, the semiperimeter is:

📌 A = r(a + b + c - c) = r(a + b - c) + rc? \quad \text{(Not helpful directly)}

📌 Instead, recall a known formula for a right triangle:

📌 Also, area \(A = r s\), so:

📌 \frac{A}{r^2} = \frac{s}{r} = \frac{\frac{a + b + c}{2}}{\frac{a + b - c}{2}} = \frac{a + b + c}{a + b - c}

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