Math Prize 2013 Problem 7
Source:
September 10, 2013
analytic geometrygeometrygeometric transformationrotationtrigonometrytrig identitiesLaw of Sines
Problem Statement
In the figure below, is an equilateral triangle.
[asy]
import graph;
unitsize(60);
axes("", "", (0, 0), (1.5, 1.5), EndArrow);
real w = sqrt(3) - 1;
pair A = (1, 1);
pair B = (0, w);
pair C = (w, 0);
draw(A -- B -- C -- cycle);
dot(Label("", A, NE), A);
dot(Label("", B, W), B);
dot(Label("", C, S), C);
[/asy]
Point has coordinates , point is on the positive -axis, and point is on the positive -axis. What is the area of ?