1994 AHSME Problems/Problem 18

Revision as of 22:07, 27 June 2014 by TheMaskedMagician (talk | contribs) (Created page with "==Problem== Triangle <math>ABC</math> is inscribed in a circle, and <math>\angle B = \angle C = 4\angle A</math>. If <math>B</math> and <math>C</math> are adjacent vertices of a ...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem

Triangle $ABC$ is inscribed in a circle, and $\angle B = \angle C = 4\angle A$. If $B$ and $C$ are adjacent vertices of a regular polygon of $n$ sides inscribed in this circle, then $n=$ [asy] draw(Circle((0,0), 5)); draw((0,5)--(3,-4)--(-3,-4)--cycle); label("A", (0,5), N); label("B", (-3,-4), SW); label("C", (3,-4), SE); dot((0,5)); dot((3,-4)); dot((-3,-4)); [/asy] $\textbf{(A)}\ 5 \qquad\textbf{(B)}\ 7 \qquad\textbf{(C)}\ 9 \qquad\textbf{(D)}\ 15 \qquad\textbf{(E)}\ 18$

Solution