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the westin hilton head island resort & spa - Coaching Toolbox

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 The radius $ r $ of the incircle is given by:

📌 where $ A $ is the area and $ s $ is the semi-perimeter.

📌 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 $.

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