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📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 For a right triangle, the radius \( r \) of the inscribed circle can be calculated using the formula:

📌 \[ r = \frac{a + b - c}{2} \]

📌 where \( a \) and \( b \) are the legs and \( c \) is the hypotenuse. First, compute the hypotenuse \( c \):

📌 \[ c = \sqrt{a^2 + b^2} = \sqrt{5^2 + 12^2} = \sqrt{25 + 144} = \sqrt{169} = 13 \text{ meters} \]

📌 Substitute the values into the formula for the radius:

📌 \[ r = \frac{5 + 12 - 13}{2} = \frac{4}{2} = 2 \text{ meters} \]

📌 Thus, the radius of the inscribed circle is \(\boxed{2}\) meters.

📌 Question:** A flood risk manager is designing a circular retention pond within a square plot to improve drainage in New Orleans. If the square plot measures 20 meters on each side, what is the circumference of the largest possible circle that can fit inside the square?

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