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Home » W = \int_C \vecF \cdot d\vecr - AIKO, infinite ways to autonomy.

W = \int_C \vecF \cdot d\vecr - AIKO, infinite ways to autonomy.

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 Question: An electrical engineer designs a high-voltage transmission tower base shaped like a regular hexagon with a side length of 8 meters. What is the radius of the circumcircle surrounding the hexagon, in meters?

📌 Solution: A regular hexagon can be divided into 6 equilateral triangles, each with side length equal to the radius of the circumcircle. Since the side length of the hexagon is 8 meters, the distance from the center to any vertex (the circumradius) is also 8 meters.

📌 This is a well-known geometric property: in a regular hexagon, the side length equals the circumradius.

📌 Therefore, the radius of the circumcircle is $ 8 $ meters.

📌 Question: A right triangle represents the voltage decay path in a high-power transmission line, with hypotenuse $ z $ and inradius $ c $. If the area of the incircle is half the area of the triangle, what is the ratio of $ c $ to $ z $?

📌 Solution: Let the right triangle have legs $ a $, $ b $, and hypotenuse $ z $. The area $ A $ is:

📌 But we are told the area of the incircle is half the area of the triangle:

📌 Substitute into the earlier equation:

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