Maximum Tangent
Source: AMC 12 2008A #24
February 17, 2008
trigonometryanalytic geometrygeometrycircumcircleHMMTexterior angletrig identities
Problem Statement
Triangle has \angle C \equal{} 60^{\circ} and BC \equal{} 4. Point is the midpoint of . What is the largest possible value of ?
(A) \ \frac {\sqrt {3}}{6} \qquad (B) \ \frac {\sqrt {3}}{3} \qquad (C) \ \frac {\sqrt {3}}{2\sqrt {2}} \qquad (D) \ \frac {\sqrt {3}}{4\sqrt {2} \minus{} 3} \qquad (E)\ 1