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fergus falls swap and shop - Coaching Toolbox

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 The radius $ c $ of the incircle of a right triangle is given by:

📌 We aim to express this in terms of $ z $ and $ c $. From the identity:

📌 Solution: When a square is inscribed in a circle, the diagonal of the square equals the diameter of the circle. The diameter is:

📌 Question: A circle is inscribed in a right triangle with legs 9 cm and 12 cm. Find the radius of the inscribed circle.

📌 Solution: Let the legs be $ a = 9 $, $ b = 12 $, and hypotenuse $ c $. First compute $ c $:

📌 Solution: Let the triangle have legs $ a = 15 $, $ b $, and hypotenuse $ h $. The inradius $ r $ of a right triangle is:

📌 Solution: For an equilateral triangle circumscribed about a circle (i.e., the incircle has radius $ r = 6 $), the relationship between the side $ s $ and the inradius is:

📌 Question: The perimeter of a right triangle is 48 cm, and its inradius is 6 cm. Find the area of the triangle.

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