2016 · Q42
If a square of side x and an equilateral triangle of side y are inscribed in a circle, then what is the ratio of x² to y²?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A{2/3}
- B{3/2}
- C3{2}
- D{2}3
Explanation
Note: the options render fractions poorly ('{2/3}' = 2/3). For the square, diagonal = 2R gives x = √2·R, so x² = 2R². For the equilateral triangle, R = y/√3, so y² = 3R². Hence x²/y² = 2/3 (option A).