We present a calculation of the angular size of the circles in the CMB predicted by Penrose on the basis of his Conformal Cyclic Cosmology. If these circles are detected, the existence of an upper limit on their angular radius would provide a challenge for inflation.Keywords: Conformal cyclic cosmology; circles in the CMB Penrose has described a radical new view of the universe, Conformal Cyclic Cosmology, in talks and articles over the past five or six years [1], [2], with the fullest account in the book [3]. At an early stage, he remarked that a prediction of CCC was that there should be circular structures observable in the CMB arising from events late in conformal time in the previous aeon. Late in conformal time, the content of the universe according to CCC is radiation and supermassive black holes, and the only significant events are black-hole mergers which give rise to sharp bursts of gravitational radiation. This radiation travels from one aeon to the next and perturbs the matter distribution early in the next aeon, which in turn produces circular perturbations in the observed CMB. In two recent articles [4], [5], he and Gurzadyan claim that these circles can be observed in the CMB as circles with significantly lower variance in the temperature. This claim is controversial and a number of authors have disagreed with the statistical significance of the findings of Penrose and Gurzadyan [6], [7], [8], [9].In this article, we do not propose to enter the debate about whether the circles have in fact been observed, but rather to suppose that Penrose's picture of CCC is correct in order to follow the consequences further. Subject to simple assumptions which are made explicit, we present a short calculation of the angular sizes of circles of the kind hypothesised by Penrose and show that there is an upper limit to their angular radius of around 21 degrees. We 1