Circle Ques 58
- 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: 58.$\frac{a^{2}}{6}$ sq unit
Solution:
Formula:
In an equilateral triangle, the radius of the incircle
$$ \begin{alignedat} & =\frac{1}{3} \times \text { median of the triangle } \\ & =\frac{1}{3} \sqrt{a^{2}-\frac{a^{2}}{4}}=\frac{1}{3} \sqrt{\frac{4 a^{2}-a^{2}}{4}}=\frac{a}{2 \sqrt{3}} \end{aligned} $$
Therefore, the area of the square inscribed in this circle
$$ 2(\text { radius of circle })^{2}=\frac{2 a^{2}}{12}=\frac{a^{2}}{6} \text { sq unit } $$
BETA
