Question

ABC is an equilateral triangle of side 6 cm. If a circle of radius 1 cm is moving inside and along the sides of the triangle, then locus of the centre of the circle is an equilateral triangle of side_______.

• A. 5 cm
• B. 4 cm
• C. $(6-2\sqrt{3})cm$
• D. $(3+\sqrt{3})cm$

Answer 1

Answer: (C)

$(6-2\sqrt{3})cm$

Since,

$\tan {30}^0=\frac{1}{x}$

$\Rightarrow \frac{1}{\sqrt{3}}=\frac{1}{x}$

$\Rightarrow x=\sqrt{3}$

$\therefore sideofsmall\Delta =6-2x=6-2\sqrt{3}$

Hence, option $\left(C\right)$ is correct answer.