Re: HSC 2013 4U Marathon
Let the vertices of the inner quadrilateral on red be z1, z2, z3, z4 and let a = cis(pi/4)/sqrt(2). Then we can find p = z1 + a(z3-z1), etc; multiplying r-q by i and subtracting it from s-p gives 0 (if we note that a-ia = 1 and a+ia = i) so equal length and perpendicular.