Question : The radius of the incircle of an equilateral $\Delta$ ABC of side $2\sqrt{3}$ cm is $x$ cm. The value of $x$ is:
Option 1: $\frac{1}{3}$
Option 2: $\frac{1}{2}$
Option 3: $1$
Option 4: $\sqrt{3}$
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Correct Answer: $1$
Solution : The radius of the incircle of an equilateral triangle is given by the formula $r = \frac{a}{2\sqrt{3}}$, where $a$ is the side length of the triangle. Given that the length of the sides of the equilateral triangle ABC is $2\sqrt{3}$ cm. $x = \frac{2\sqrt{3}}{2\sqrt{3}} = 1$ Hence, the correct answer is 1 cm.
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