MathDB
Well-Known Rotation Problem

Source: 2020 AMC 12A #24

January 31, 2020
AMCAMC 122020 AMC2020 AMC 12ATrianglegeometryAMC 12 A

Problem Statement

Suppose that △ABC\triangle ABC is an equilateral triangle of side length ss, with the property that there is a unique point PP inside the triangle such that AP=1AP = 1, BP=3BP = \sqrt{3}, and CP=2CP = 2. What is s?s?
<spanclass=′latex−bold′>(A)</span>1+2<spanclass=′latex−bold′>(B)</span>7<spanclass=′latex−bold′>(C)</span>83<spanclass=′latex−bold′>(D)</span>5+5<spanclass=′latex−bold′>(E)</span>22<span class='latex-bold'>(A) </span> 1 + \sqrt{2} \qquad <span class='latex-bold'>(B) </span> \sqrt{7} \qquad <span class='latex-bold'>(C) </span> \frac{8}{3} \qquad <span class='latex-bold'>(D) </span> \sqrt{5 + \sqrt{5}} \qquad <span class='latex-bold'>(E) </span> 2\sqrt{2}
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