Two groups [3,4] have confirmed the results of our paper concerning the actual existence of low variance circles in the cosmic microwave background (CMB) sky. They also point out that the effect does not contradict the LCDM model - a matter which is not in dispute. We point out two discrepancies between their treatment and ours, however, one technical, the other having to do with the very understanding of what constitutes a Gaussian random signal. Both groups simulate maps using the CMB power spectrum for LCDM, while we simulate a pure Gaussian sky plus the WMAP's noise, which points out the contradiction with a common statement  that "CMB signal is random noise of Gaussian nature". For as it was shown in , the random component is a minor one in the CMB signal, namely, about 0.2. Accordingly, the circles we saw are a real structure of the CMB sky and they are not of a random Gaussian nature. Although the structures studied certainly cannot contradict the power spectrum, which is well fitted by LCDM model, we particularly emphasize that the low variance circles occur in concentric families, and this key fact cannot be explained as a purely random effect. It is, however a clear prediction of conformal cyclic cosmology.