MathDB
1993 AMC 12 #23 - Angles in a Circle

Source:

January 2, 2012
trigonometrygeometrytrig identitiesLaw of SinesAMC

Problem Statement

Points A,B,CA, B, C and DD are on a circle of diameter 11, and XX is on diameter AD‾\overline{AD}. If BX=CXBX=CX and 3∠BAC=∠BXC=36∘3 \angle BAC=\angle BXC=36^{\circ}, then AX=AX= [asy] draw(Circle((0,0),10)); draw((-10,0)--(8,6)--(2,0)--(8,-6)--cycle); draw((-10,0)--(10,0)); dot((-10,0)); dot((2,0)); dot((10,0)); dot((8,6)); dot((8,-6)); label("A", (-10,0), W); label("B", (8,6), NE); label("C", (8,-6), SE); label("D", (10,0), E); label("X", (2,0), NW); [/asy] <spanclass=′latex−bold′>(A)</span> cos⁡6∘cos⁡12∘sec⁡18∘<spanclass=′latex−bold′>(B)</span> cos⁡6∘sin⁡12∘csc⁡18∘<spanclass=′latex−bold′>(C)</span> cos⁡6∘sin⁡12∘sec⁡18∘<spanclass=′latex−bold′>(D)</span> sin⁡6∘sin⁡12∘csc⁡18∘<spanclass=′latex−bold′>(E)</span> sin⁡6∘sin⁡12∘sec⁡18∘ <span class='latex-bold'>(A)</span>\ \cos 6^{\circ}\cos 12^{\circ} \sec 18^{\circ} \qquad<span class='latex-bold'>(B)</span>\ \cos 6^{\circ}\sin 12^{\circ} \csc 18^{\circ} \qquad<span class='latex-bold'>(C)</span>\ \cos 6^{\circ}\sin 12^{\circ} \sec 18^{\circ} \\ \qquad<span class='latex-bold'>(D)</span>\ \sin 6^{\circ}\sin 12^{\circ} \csc 18^{\circ} \qquad<span class='latex-bold'>(E)</span>\ \sin 6^{\circ} \sin 12^{\circ} \sec 18^{\circ}
Back to ProblemsView on AoPS