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when did world war i start - Coaching Toolbox

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 To find the shortest altitude, we first note that the shortest altitude corresponds to the longest side, since the altitude is inversely proportional to the base length for a fixed area.

📌 Let the triangle have sides $ a = 7 $, $ b = 8 $, and $ c = 9 $.

📌 We begin by computing the area of the triangle using Herons formula.

📌 Now, to find the altitude $ h $ corresponding to the longest side $ c = 9 $:

📌 Since the rectangle is inscribed in the circle, its diagonal is the diameter of the circle.

📌 The diagonal $ d $ of the rectangle is:

📌 So, the diameter of the circle is 13 m, and the radius is:

📌 Question: A chemical engineer is modeling the cross-section of a cylindrical bioreactor vessel as a circle. A right triangle with legs of length $ a $ and $ b $ is inscribed in the circle, with the hypotenuse as the diameter. If the inradius of the triangle is $ r $, what is the ratio of the area of the incircle to the area of the triangle?

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