MathDB
Triangle and simple line

Source: 2001 AMC-12 #24

December 4, 2005
geometrytrigonometryfunctioncircumcircleAMCUSA(J)MOUSAMO

Problem Statement

In ABC \triangle ABC, \angle ABC \equal{} 45^\circ. Point D D is on BC \overline{BC} so that 2 \cdot BD \equal{} CD and \angle DAB \equal{} 15^\circ. Find ACB \angle ACB. [asy] pair A, B, C, D; A = origin; real Bcoord = 3*sqrt(2) + sqrt(6); B = Bcoord/2*dir(180); C = sqrt(6)*dir(120); draw(A--B--C--cycle); D = (C-B)/2.4 + B; draw(A--D);
label("AA", A, dir(0)); label("BB", B, dir(180)); label("CC", C, dir(110)); label("DD", D, dir(130)); [/asy] <spanclass=latexbold>(A)</span> 54<spanclass=latexbold>(B)</span> 60<spanclass=latexbold>(C)</span> 72<spanclass=latexbold>(D)</span> 75<spanclass=latexbold>(E)</span> 90 <span class='latex-bold'>(A)</span> \ 54^\circ \qquad <span class='latex-bold'>(B)</span> \ 60^\circ \qquad <span class='latex-bold'>(C)</span> \ 72^\circ \qquad <span class='latex-bold'>(D)</span> \ 75^\circ \qquad <span class='latex-bold'>(E)</span> \ 90^\circ