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📅 May 16, 2026 👤 scraface

May 16, 2026

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📌 This circumference defines the full loop the drone follows, optimizing coverage over the rectangular zone.

📌 Question: A historian analyzing ancient geometric instruments discovers a triangular tablet with integer side lengths forming a right triangle, where the hypotenuse is $ z $ and the inradius is $ c $. If $ z = 25 $ and $ c = 5 $, what is the ratio of the area of the inscribed circle to the area of the triangle?

📌 Solution: For a right triangle with legs $ a $, $ b $, hypotenuse $ z = 25 $, and inradius $ c = 5 $, we use the formula for the inradius of a right triangle:

📌 Substitute $ c = 5 $ and $ z = 25 $:

📌 We also have $ a + b = 35 $. Square both sides:

📌 This ratio indirectly supports ergonomic design in ancient measuring devices, where geometric harmony maximized precision.

📌 Solution: The area $ A $ of an equilateral triangle with side $ s $ is:

📌 New side length: $ s = 16 - 4 = 12 $ cm. New area:

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