2018 · Q72
A circle is inscribed in an equilateral triangle of side of length l. The area of any square inscribed in the circle is
Elementary MathematicsCircles
- Al22/{l^2}{2}
- B3l24/{√{3}l^2}{4}
- Cl42/{l^4}{2}
- Dl26/{l^2}{6}
Explanation
The inradius of the equilateral triangle is l/(2 sqrt(3)), which is the circle's radius r. A square inscribed in the circle has diagonal 2r = l/sqrt(3). Its area is (diagonal^2)/2 = (l^2/3)/2 = l^2/6. Hence option D.