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Home » So the 2D coordinate is $(4, 3)$. - SUpost

So the 2D coordinate is $(4, 3)$. - SUpost

📅 July 6, 2026 👤 scraface

Jul 06, 2026

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📌 Thus, the shortest distance from the center to the path is $ \boxed{4} $ meters.

📌 Question: A robotics engineer is designing a triangular linkage mechanism where the sides measure 7 cm, 10 cm, and 13 cm. What is the radius of the inscribed circle in this triangle?

📌 Let the triangle have side lengths $ a = 7 $, $ b = 10 $, $ c = 13 $. First, compute the semi-perimeter $ s $:

📌 s = \frac{a + b + c}{2} = \frac{7 + 10 + 13}{2} = \frac{30}{2} = 15

📌 Now, use Heron’s formula to find the area $ A $:

📌 A = \sqrt{s(s - a)(s - b)(s - c)} = \sqrt{15(15 - 7)(15 - 10)(15 - 13)} = \sqrt{15 \cdot 8 \cdot 5 \cdot 2}

📌 A = \sqrt{15 \cdot 8 \cdot 10} = \sqrt{1200} = \sqrt{400 \cdot 3} = 20\sqrt{3}

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