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2021 AMC 12C Question 13

AMC12 · 2021 AMC 12C

Question 13

The angle bisector of the acute angle formed at the origin by the graphs of the lines $y = x$ and $y = 3x$ has equation $y = kx.$ What is $k?$
  1. $\dfrac{1 + \sqrt{5}}{2}$
  2. $\dfrac{1 + \sqrt{7}}{2}$
  3. $\dfrac{2 + \sqrt{3}}{2}$
  4. $2$
  5. $\dfrac{2 + \sqrt{5}}{2}$