AP EAMCET · Maths · Properties of Triangles
If a circle is inscribed in an equilateral triangle of side a, then the area of any square (in sq. units) inscribed in this circle is
- A \(\frac{2 a^2}{3}\)
- B \(\sqrt{3} \frac{a^2}{2}\)
- C \(\frac{a^2}{2 \sqrt{3}}\)
- D \(\frac{a^2}{6}\)
Answer & Solution
Correct Answer
(D) \(\frac{a^2}{6}\)
Step-by-step Solution
Detailed explanation
Area of \(\triangle A B C(\Delta)=\frac{\sqrt{3}}{4} a^2\), Semi-perimeter of \(\triangle A B C(s)=\frac{3 a}{2}\) Radius (r) \(=\frac{\Delta}{s}=\frac{a}{2 \sqrt{3}}\) Diagonal of square PQRS \(=2 \times \frac{a}{2 \sqrt{3}}=\frac{a}{\sqrt{3}}\) Area of square…
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\(\begin{array}{lll}
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\hline
\end{array}\)
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