This paper is devoted to determine a lower bound for the ratio of self-similarity. Let \(f(z)=e^{2\pi i\theta}z+z^2\), where \(\theta\) is a quadratic irrational. The authors show that if \(\theta=\frac{\sqrt 5-1}{2}\) is the golden mean, then there exists a triangle contained in the Siegel disk, and with one vertex at the critical point.