MathDB
Minimum Length of Broken Line

Source: 2014 AMC 12A #20

February 5, 2014
geometrygeometric transformationreflectiontrigonometryinequalitiesAsymptotetrig identities

Problem Statement

In △BAC\triangle BAC, ∠BAC=40∘\angle BAC=40^\circ, AB=10AB=10, and AC=6AC=6. Points DD and EE lie on AB‾\overline{AB} and AC‾\overline{AC} respectively. What is the minimum possible value of BE+DE+CDBE+DE+CD?
<spanclass=′latex−bold′>(A)</span>63+3<spanclass=′latex−bold′>(B)</span>272<spanclass=′latex−bold′>(C)</span>83<spanclass=′latex−bold′>(D)</span>14<spanclass=′latex−bold′>(E)</span>33+9<span class='latex-bold'>(A) </span>6\sqrt 3+3\qquad <span class='latex-bold'>(B) </span>\dfrac{27}2\qquad <span class='latex-bold'>(C) </span>8\sqrt 3\qquad <span class='latex-bold'>(D) </span>14\qquad <span class='latex-bold'>(E) </span>3\sqrt 3+9\qquad
Back to ProblemsView on AoPS