Bereishit 18:1
VaYera elav - [Hashem] Appeared to him. 
The phrase nimolu [ito], were circumcised [with him] (17:27), is juxtaposd with [Hashem] appeared to him.  This teaches that G-d appeared because of the patient; to visit him.
Rabbi Chama explains the term kechom hayom, in the heat of the day - that it was the third day following Avraham's circumcision and the Holy One, Baruch Hu, came to inquire [regarding the welfare] of Avraham.  The Holy One, Baruch Hu, took the sun out of its sheath, i.e., He made it blaze intensely, so that the righteous Avraham would not be bothered with guests (Bava Metzia 86).  Now, this latter discussion does not explicitly mention anything about sickness; rather, G-d visited Avraham in honor of the mitzvah of circumcision that Avraham had performed.  Based on this teaching, other editions (as well as the manuscript version used by Shoham Yakar) have the word hamilah, the circumcision, in place of hacholeh, the patient.  And, it is based on this teaching that the Baal HaTurim finds an allusion to circumcision in the gematria of vayera elav.
Alternatively:  The juxtaposition of were circumcised with him with while he was sitting at the entrance of the tent in the heat of the day can be explained in terms of our Sages' statement that Avraham sits at the entrance to Gehinnom (Hell, expressed here as the heat of the day), and does not allow anyone who has been circumcised to enter, except one who has had relations with a gentile woman, for he has extended his foreskin and therefore Avraham cannot recognize that he is circumcised.
This concept is reflected by the masoretic note on the word kechom, which means that it appears four times in the Tanach:
  1. at the entrance of the tent in the heat of the day (Bereishit 18:1)
  2. when the sun becomes hot  (1 Shmuel 11:9)
  3. like the clear heat in sunlight (Yeshayahu 18:4)
  4. and they arrived in the heat of the day at the home of Ish-boshet (2Shmuel 4:5)
This intimates that Avraham would seat himself at the entrance of the tent [i.e., Gehinnom], and not allow a person who is circumcised to enter into [the place called] the heat of the day.  Instead, [he brings them to] the clear heat of the sunlight, i.e., Gan Eden, as alluded to in the verse, but Hashem shall be unto you an everlasting light (Yeshayahu 60:19).  Nevertheless, Ish-boshet, literally, a shameful man, i.e., one who has had relations with a gentile woman, for there is no greater shame than that of a Jewish man who has relations with a gentile woman, shall come in the heat of the day, i.e., shall enter Gehinnom, of which it is written, Behold, the day comes that shall brun as an oven (Malachi 3:19).
This concept is fruther reflected in the gematria of the phrase kechom hayom, in the heat of the day (129), which is equivalent to that of zehu beGehinnom, this is in Gehinnom; and is equal to to the gematria of dam milah, blood of circumcision.
Vehineh sheloshah - And Behold!  Three [men].
The gematria of this phrase (701) is equal to that of the phrase These are Michael, Gavriel and Rafael.  The Sages identify the three visitors as these three angels: Michael came to inform Sarah that she would bear a child; Rafael came to heal Avraham; and Gavriel came to overturn Sedom (Bava Metzia 86b; Rashi)
Verachatzu ragleichem -And wash your feet.
From this our Sages derived that Avraham suspected [his visitors of] idolatry.  This can be understood from Lot's offer: First he invited them to spend the night and then to wash their feet (19:2).  Avraham, however, first invited them to wash their feet and then to stay as his guests.  This teaches that Avraham suspected that they were Arabs [i.e., desert dwellers (see Rashi to Yirmeyahu 3:2) who worshiped the dust on their feet] and would bring the object of their idolatry into his home.
-Baal HaTurim