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celebrities who lost homes in fire 2025 - Anadea

📅 May 16, 2026 👤 scraface

May 16, 2026

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📌 Question: An archaeologist discovers a triangular stone slab with side lengths 13 cm, 14 cm, and 15 cm. What is the radius of the inscribed circle?

📌 Solution: To find the radius $r$ of the inscribed circle of a triangle with sides $a = 13$, $b = 14$, and $c = 15$, we use the formula:

📌 r = \frac{A}{s}

📌 where $A$ is the area of the triangle and $s$ is the semi-perimeter:

📌 s = \frac{a + b + c}{2} = \frac{13 + 14 + 15}{2} = 21

📌 Using Heron’s formula for area:

📌 r = \frac{84}{21} = 4

📌 $$Question: What is the largest possible value of $\gcd(a,b)$, if the sum of two positive integers $a$ and $b$ is $1000$ and both $a$ and $b$ are divisible by a perfect square greater than $1$?

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