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to cut one's nose to spite one's face - Parker Core Knowledge

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 Question: A paleobotanist models a fossilized leaf vein pattern as a right triangle with hypotenuse $ z $ and inradius $ c $. What is the ratio of the area of the incircle to the area of the triangle?

📌 Let the triangle be a right triangle with hypotenuse $ z $ and inradius $ c $.

📌 The area $ A $ of a right triangle with legs $ a $, $ b $, and hypotenuse $ z $ is:

📌 The inradius $ c $ of a right triangle is:

📌 We express the ratio $ R $ of the incircle area to triangle area:

📌 Lets express $ ab $ in terms of $ z $ and $ c $.

📌 Thus, the ratio of the area of the incircle to the area of the triangle is:

📌 Question: A climatologist models a triangular weather system with side lengths of 13 km, 14 km, and 15 km. What is the length of the median to the side of length 14 km?

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