Circle 3 Question 18

18. A circle is inscribed in an equilateral triangle of side $a$. The area of any square inscribed in this circle is… .

(1994, 2M)

Show Answer

Answer:

Correct Answer: 18. $\frac{a^{2}}{6}$ sq unit

Solution:

  1. In an equilateral triangle, the radius of incircle

$$ \begin{aligned} & =\frac{1}{3} \times \text { median of the triangle } \\ & =\frac{1}{3} \sqrt{a^{2}-\frac{a^{2}}{4}}=\frac{1}{3} \sqrt{\frac{4 a^{2}-a^{2}}{4}}=\frac{a}{2 \sqrt{3}} \end{aligned} $$

Therefore, area of the square inscribed in this circle

$$ =2(\text { radius of circle })^{2}=\frac{2 a^{2}}{4 \cdot 3}=\frac{a^{2}}{6} \text { sq unit } $$



NCERT Chapter Video Solution

Dual Pane