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Source: 2021 AMC 12A Fall #13

November 11, 2021
AMCAMC 12AMC 12 Atrigonometry

Problem Statement

The angle bisector of the acute angle formed at the origin by the graphs of the lines y=xy=x and y=3xy=3x has equation y=kxy=kx. What is kk?
<spanclass=′latex−bold′>(A)</span> 1+52<spanclass=′latex−bold′>(B)</span> 1+72<spanclass=′latex−bold′>(C)</span> 2+32<spanclass=′latex−bold′>(D)</span> 2<spanclass=′latex−bold′>(E)</span> 2+52<span class='latex-bold'>(A)</span> \: \frac{1+\sqrt{5}}{2} \qquad <span class='latex-bold'>(B)</span> \: \frac{1+\sqrt{7}}{2} \qquad <span class='latex-bold'>(C)</span> \: \frac{2+\sqrt{3}}{2} \qquad <span class='latex-bold'>(D)</span> \: 2\qquad <span class='latex-bold'>(E)</span> \: \frac{2+\sqrt{5}}{2}
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