Multiple choice

If an equilateral triangle is inscribed in the circle ${x}^{2}+{y}^{2}={k}^{2}$ the length of each side is equal to

  1. $k/\surd 3$
  2. $k\sqrt 3$
  3. $K$
  4. $2K$
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B Correct answer
Explanation

The circle has radius k. An equilateral triangle inscribed in a circle has side length sqrt(3) times its circumradius, so each side measures k sqrt(3).

AI explanation

The equation x^2 + y^2 = k^2 represents a circle centered at the origin with radius k. When an equilateral triangle is inscribed in a circle, the radius of the circle relates to the side of the triangle by the formula R = side / sqrt(3). Substituting R = k into this formula gives k = side / sqrt(3). Solving for the side yields the length of side = k * sqrt(3).

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