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Home » This Midnight Training Session Proved Rousey Still Belongs in the Headlines! - Abbey Badges

This Midnight Training Session Proved Rousey Still Belongs in the Headlines! - Abbey Badges

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 Thus, the radius of the inscribed circle is $ \boxed{\dfrac{4\sqrt{3}}{3}} $ cm.

📌 Question: An entomologist observes a spiderweb forming a perfect equilateral triangle with side length 12 cm. What is the area of the circle that circumscribes this triangle?

📌 For an equilateral triangle of side length $ s = 12 $, the circumradius $ R $ is given by the formula:

📌 R = \frac{s}{\sqrt{3}}

📌 But more accurately, the correct formula for the circumradius of an equilateral triangle is:

📌 R = \frac{s}{\sqrt{3}} \cdot \frac{2}{3} \cdot \text{height} = \frac{s}{\sqrt{3}} \cdot \frac{2}{3} \cdot \frac{\sqrt{3}}{2}s = \frac{s}{\sqrt{3}} \cdot \frac{\sqrt{3}}{2} \cdot \frac{2}{3} \cdot s

📌 Actually, the standard formula is:

📌 R = \frac{s}{2 \sin A} = \frac{s}{2 \sin 60^\circ} = \frac{12}{2 \cdot \frac{\sqrt{3}}{2}} = \frac{12}{\sqrt{3}} = 4\sqrt{3}

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