Simple cevian-related problem
Source: Canadian Mathematical Olympiad - 1986 - Problem 1.
July 3, 2011
geometrytrigonometrygeometry proposed
Problem Statement
In the diagram line segments and are of length 1 while angles and are and respectively. Find .[asy]
import geometry;
import graph;unitsize(1.5 cm);pair A, B, C, D;B = (0,0);
D = (3,0);
A = 2*dir(120);
C = extension(B,dir(30),A,D);draw(A--B--D--cycle);
draw(B--C);
draw(arc(B,0.5,0,30));label("", A, NW);
label("", B, SW);
label("", C, NE);
label("", D, SE);
label("", (0.8,0.2));
label("", (0.1,0.5));perpendicular(B,NE,C-B);
[/asy]