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Home » For any triangle, the radius \( r \) of the inscribed circle is given by: - Sterling Industries

For any triangle, the radius \( r \) of the inscribed circle is given by: - Sterling Industries

📅 April 18, 2026 👤 scraface

Apr 18, 2026

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📌 We first calculate the area using Herons formula. The semi-perimeter $ s $ is:

📌 The length of the shortest altitude is:

📌 Question: A pharmaceutical research team models the diffusion of a drug in a triangular region with side lengths of 7 cm, 24 cm, and 25 cm. What is the radius of the inscribed circle in cm?

📌 The radius of the inscribed circle is:

📌 So the diameter is 13 cm, and the circumference is:

📌 Set this equal to zero and solve for $x$:

📌 Solution: To ensure diversification, the vectors must be orthogonal, so their dot product is zero:

📌 Solution: Start by expanding both terms:

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This is allowed since unit vectors can be identical.
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