COMC 2011 Problem 4
Source:
November 4, 2012
ratio
Problem Statement
In the figure, AQPB and ASRC are squares, and AQS is an equilateral triangle. If QS = 4 and BC = x, what is the value of x?
[asy]
unitsize(16);
pair A,B,C,P,Q,R,T;
A=(3.4641016151377544, 2);
B=(0, 0);
C=(6.928203230275509, 0);
P=(-1.9999999999999991, 3.464101615137755);
Q=(1.4641016151377544, 5.464101615137754);
R=(8.928203230275509, 3.4641016151377544);
T=(5.464101615137754, 5.464101615137754);
dot(A);dot(B);dot(C);dot(P);
dot(Q);dot(R);dot(T);
label("", (3.4641016151377544, 2),E);
label("", (0, 0),S);
label("", (6.928203230275509, 0),S);
label("", (-1.9999999999999991, 3.464101615137755), W);
label("", (1.4641016151377544, 5.464101615137754),N);
label("", (8.928203230275509, 3.4641016151377544),E);
label("", (5.464101615137754, 5.464101615137754),N);
draw(B--C--A--B);
draw(B--P--Q--A--B);
draw(A--C--R--T--A);
draw(Q--T--A--Q);
label("", (3.4641016151377544, 0), S);
label("", (Q+T)/2, N);[/asy]