ɐnˈʌðɚ spˈɛʃəl kˈeɪs ɪz ðə vˈɪlɑːɹsˌoʊ sˈɜːkəlz, ɪnwˌɪtʃ ðɪ ˌɪntɚsˈɛkʃən ɪz ɐ sˈɜːkəl dᵻspˈaɪt ðə lˈæk ʌv ˌɛni ʌvðɪ ˈɑːbviəs sˈɔːɹts ʌv sˈɪmətɹi ðæt wʊd ɛntˈeɪl ɐ sˈɜːkjʊlɚ kɹˈɔssˈɛkʃən.
Another special case is the Villarceau circles, in which the intersection is a circle despite the lack of any of the obvious sorts of symmetry that would entail a circular cross-section.