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Week 0: 1 infected - Imagemakers

📅 April 30, 2026 👤 scraface

Apr 30, 2026

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📌 Question:** A mammalogist studying the Arctic tundra uses a triangular net to trap tracks of mammals for observation. The net is in the shape of a right triangle with legs measuring 5 meters and 12 meters. What is the radius of the circle that can be inscribed within this triangle?

📌 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.

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