<div dir="ltr"><div>The Avudraham does indeed state that even if it would fall on Shabbos we would fast becasue of B'etzem Hayom Hazeh. The Ohr Sameach to Hilchos Taaniyos 5 has a fascinating source for this from Eruvin 40b, where the Gemara has a Safek about a Bar Bei Rav who is fasting on Friday, whether he should complete it. The question is why the Gemara had no such Safek regarding a Taans Tzibbur, and the OS answers that during the time of the Amoraim Kidush Hachodesh was Al Pi Cheshbon, and the only Taanis Tzibur that can fall out on Friday is Asarah B'teves. Since one would fast Asarah B'teves even on Shabbos, there was no question that one would be Mashlim it from Friday into Shabbos.</div>
<div> </div>
<div>The Sevaros for the Avudraham revolve around the allowance for Taanis Chalom on Shabbos. See Chasam Sofer in his Drush to 7 Adar (Yom Din on Binyan Beis Hamikdash in the future), R' Chaim (stencil Simman 44 - it has to be fasted today), and the Ohr Sameach there (only Assur D'oraysa if fasting MeEis L'eis, and the B'etzem... of the Avudraham is just to distinguish it from Tzom Gedalia and 17 Tammuz; Tisha B'Av would be Assur MiDeorysa).</div>
<div> </div>
<div>[All the above taken from recently published Sefer Minchas Aharon on Taaniyos Tzibbur]</div></div>