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Making a bris Milah on Taanis Esther:
One may not make a Seudas Mitzvah for the public on Taanis Esther and the meal is hence to take place after the fast.
If the fast was pushed up to Thursday: In the event that the fast fell on Shabbos and was hence pushed up to Thursday, then one who has a Bris taking place on Thursday is to make the meal that day, and is to make up the fast on Friday. All those invited may participate in the meal, even if they are more than ten people, and even if the meal takes place in the morning. They are all however to make up the fast the next day, with exception to the Baalei Bris which are exempt from making up the fast. However some Poskim argue on the above and rule that the meal is to take place on Thursday night after the fast. Practically some Poskim rule like this latter opinion, while others rule one may be lenient like the first opinion.
 See Rama 686/2; M”A 559/11 regarding Tishe Beav and all the other 4 Taaneisim and so rules: Radbaz 2/35; M”B 559/35; Beis David 347; Erech Hashulchan 550/1; Poskim brought in Kaf Hachaim 549/5 and 10; See Piskeiy Teshuvos 559/9
 Rama 686/2
Regarding Tishe Beav and the other fasts of scripture: In the event that the fast fell on Shabbos and was hence pushed off to Sunday, then one who has a Bris taking place on Sunday is not required to fast until night. [See Michaber 559/9 regarding Tishe Beav Nidche and certainly the same applies for the other four fast days that are Nidche and so rule: Elya Raba; Chayeh Adam; M”B 559/37; Shaareiy Tziyon 559/39; Degul Merivava; Heishiv Moshe 36; Yeshuos Yaakov 559/5; Kitzur SHU”A 125/8; Ben Ish Chaiy Shoftim 17; Igros Moshe 4/69-4; Yabia Omer 1/34; See Piskeiy Teshuvos 559/9 footnote 74] See however the M”A 559/11 that brings in the name of the Kneses Hagedola that the custom is to be stringent regarding all fasts, even Nidche, and to fast until night as usual.
 Rama ibid
 M”B 686/7; Shaar Hatziyon 686/13
Regarding the other fasts of scripture: The meal must take place after Mincha. [See M”A 559/13; M”B 559/37]
 M”B ibid; Kaf Hachaim 686/28 in name of Chayeh Adam 155/3 and Kitzur SHU”A 141/3 regarding the Baal Bris
 Taz 686/2; Elya Raba 686/6 brought in Kaf Hachaim 686/27; M”B 686/7; Regarding the four fasts of scripture so rules: M”A 559/11 in the name of the Kneses Hagedola that the custom is to be stringent regarding all fasts, even Nidche, and to fast until night as usual.
 Chayeh Adam 155/3 based on that the custom is like the Taz as we have never seen a meal done during the day of the fast. So rules also Kitzur SHU”A 141/3; Kaf Hachaim 686/27
 PM”G 686 M”Z 2; Mor Uketzia; Shvus Yaakov brought in M”B 686/7