a circle is inscribed in a equilateral triangle of side a.find the area of any square inscribed in the circle.
11It's better with trigonometry.
Inradius of the triangle is known.....now the side of the square be x, so 2x2=4r2 so x2=2r2.....where r is the inradius of the triangle.
39now ... r=\frac{a}{2\sqrt{3}}
and for any square inscribedin the circle ... we have the diagonal is twice the radius of the circle..
let the side of square be b
then \sqrt{2}b=\frac{a}{\sqrt{3}}\Rightarrow b=\frac{a}{\sqrt{6}}
so area of square =b^{2}=\frac{a^{2}}{6}
