Question : In an equilateral triangle inradius is 4 cm. What is the circumradius?
Option 1: 6 cm
Option 2: 8 cm
Option 3: 12 cm
Option 4: 2 cm
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Correct Answer: 8 cm
Solution :
The circumradius $(R)$ and inradius $(r)$ are related by the formula:
$ R = \frac{a}{\sqrt{3}}$ and $ r = \frac{a}{2\sqrt{3}}$
Where $a$ is the side of the triangle
Given: Inradius = 4 cm, we can find the side of the triangle:
$ a = 2\sqrt{3} \times r = 2\sqrt{3} \times 4 = 8\sqrt{3}\ \text{cm}$
Substituting $a$ into the formula for the circumradius, we get:
$ R = \frac{a}{\sqrt{3}} = \frac{8\sqrt{3}}{\sqrt{3}} = 8 \ \text{cm}$
Hence, the correct answer is 8 cm.
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