2023 · Q65
Let x be the area of a square inscribed in a circle of radius r and y be the area of an equilateral triangle inscribed in the same circle. Which one of the following is correct?
Elementary MathematicsCircles
- A9x² = 16y²
- B27x² = 64y²
- C36x² = 49y²
- D16x² = 21y²
Explanation
The inscribed square has diagonal 2r, side r√2 and area x = 2r². The inscribed equilateral triangle has side r√3 and area y = (√3/4)(3r²) = 3√3r²/4. Then 27x² = 108r⁴ and 64y² = 64·27r⁴/16 = 108r⁴, so 27x² = 64y² (B).