1. Bris Milah on a fast day:[1]

If a Bris falls on a fast day, then it is to take place as usual, although without food, as explained next.

Drinking the wine:[2] When a Bris is taking place on a fast day then the wine is to be given to drink to a child [who has reached the age of Chinuch[3]].

Fasting:[4] The Baal Bris [father of the child, Mohel and Sandak[5]] are all required to fast the entire day even though the Bris is taking place that day. Thus, the Seudas Mitzvah is to take place only after the fast.

Taanis Nidche-If the fast was pushed off to Sunday:[6] 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. Rather [after midday[7]] he is to Daven Mincha early. After he Davens Mincha he may then eat. The same applies for all the Baalei Bris [however not for anyone else invited to the Bris, including the Kvatrin, which must fast until night[8]]. [Nevertheless, they are not to make a large meal during the day as is normally done on the day of a Bris, and thus the main meal is to take place at night.[9]Nevertheless, despite the above ruling, some Poskim[10] rule that even on a Taanis Nidche the Baal Bris is to fast the entire day as usual, and so is the custom of certain communities.[11] However most communities are lenient in this matter as is the plain ruling in Shulchan Aruch.[12]]

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[1] See Pesakim Uteshuvos 265:17

[2] Admur 621:4 and 6 regarding Tishe Beav; Michaber 559:7; M”A 559:9; Beir Heiytiv 621:11; See Shevach Habris 18:19; Pesakim Uteshuvos 265:15

[3] See Admur 190:4; 621:5; M”A 559:9; Beir Heiytiv 621:11

Other opinions: Some Poskim rule that it may even initially be given to a Katan who is under the age of Chinuch. [2^nd opinion in Admur 190:4]

[4] M”A 559:11 regarding Tisha B’av 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

[5] Rama 559:8

[6] Michaber 559:9 regarding Tisha B’av 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; Shaar Hatziyon 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

Other opinions: The M”A 559:11 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.

[7] First opinion in M”A 559:13; M”B 559:37

Other opinions: Some Poskim rule one must delay Mincha and eating until Mincha Ketana. [2^nd opinion in M”A ibid and so concludes the M”A]

[8] M”B 559:36; P”M 559 A”A 12; This is opposed to the ruling by Taanis Esther that was Nidche to Thursday. See M”B 686:6; Kaf Hachaim 686:27

[9] M”B 559:36 based on M”A 559:11 “Today the custom is that majority of the meals take place at night”; See the following Poskim regarding Taanis Esther Nidche that the meal is to take place after the fast: Taz 686:2; Elya Raba 686:6 brought in Kaf Hachaim 686:27; M”B 686:7; 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

[10] Kneses Hagedola brought in M”A 559:11; Zechor Leavraham “Taf” brought in Kaf Hachaim 549:10; Divrei Yisrael 150; See Piskeiy Teshuvos 559:9; Regarding Taanis Esther so rules: Zera Emes 3:77; Poskim brought in Kaf Hachaim 686:28; 549:9, brought also in Piskeiy Teshuvos 686:4

[11] See Piskeiy Teshuvos ibid

[12] Poskim mentioned in first footnote on this Halacha; Piskeiy Teshuvos ibid

[13] Rama 559:8; P”M 559 A”A 12

[14] Shaareiy Teshuvah 551:15; 559:7 in name of Peri Haaretz 2:8; Birkeiy Yosef 559:6; Kaf Hachaim 559:9

[15] SSH”K 62 footnote 116; Piskeiy Teshuvos 559:9