At the beginning of Parshat Vayera, Rashi quotes Rabbi Chama Bar Chanina (Bava Metziah 86:42), who says, אותו היום יום שלישי של מילה של אברהם היה ובא הקדוש ברוך הוא לשאול אברהם “It was the third day after Avraham’s Brit and Hashem came to find out how he was feeling.” Rabbi Yisrael of Chortkov explains that this Rashi relates to the concept in Pirkei Avot that says that the world stands on three pillars: Torah, Avoda, and גמילות חסדים. Each one of our forefathers set the standard for each individual pillar. Avraham Avinu set the foundation for Gemiult Chesed. When one thinks of the Mitzva of הכנסת אורחים the first person that comes to mind is Avraham. However, after he had his Brit he could not fulfill the Mitzva of הכנסת אורחים.
During these days Avraham was considered as חשב אדם לעשות מצוה ונאנס ולא עשאה, “One who thought to fulfill a Mitzva and forcefully could not do so, and therefore was considered as one who did it regardless” (Kedushin 40). Avraham’s good will and intentions to fulfill the Mitzva of הכנסת אורחים for the past three days consumed him. Therefore, Hashem sent three angles that were created from Avraham’s powerful will and fierce determination to fulfill the Mitzva. With the appearance of the three angles in Avraham’s doorway, we learn that the visit indeed took place on the third day after Avraham’s brit.