"A son for his old age" (Genesis 21:7) - it teaches that the radiance of his features resembled his own. "At the appointed time of which God had spoken to him" (Genesis 21:2). Rabbi Yudan said: he was born at nine months, so that they would not say he was swept out of the house of Abimelech. Rabbi Chama said: at seven full months, which are nine partial ones. Rabbi Huna in the name of Rabbi Chizkiyah: he was born at midday. "Appointed time" is said here, and "appointed time" is said elsewhere, "at the going down of the sun, the appointed time of your going out from Egypt" (Deuteronomy 16:6). "And Abraham called the name of his son who was born to him, whom Sarah bore to him, Isaac" (Genesis 21:3). A decree of freedom went forth to the world. Yitzchak [Isaac]: the yod is ten, corresponding to the Ten Commandments which his children would in the future receive. The tzadi is ninety, "shall Sarah, who is ninety years old, bear a child?" (Genesis 17:17). The kof is one hundred, "shall a child be born to one who is a hundred years old?" (Genesis 17:17). The chet is eight, corresponding to the eight days of circumcision. "And Abraham circumcised his son Isaac at eight days, as God had commanded him" (Genesis 21:4); and where had He spoken? "And he who is eight days old shall be circumcised among you, every male" (Genesis 17:12).
Isaac's Face Like Abraham's and the Meaning of His Name
Yalkut Shimoni on Torah 92:2
בֵּן לִזְקֻנָּיו, מְלַמֵּד שֶׁהָיָה זִיו אִיקוּנִין שֶׁלוֹ דּוֹמֶה לוֹ. לַמּוֹעֵד אֲשֶׁר דִּבֵּר אֹתוֹ אֱלֹהִים, רַבִּי יוּדָן אָמַר לְתִשְׁעָה חֳדָשִׁים נוֹלַד שֶׁלֹּא יְהוּ אוֹמְרִים גָּרוּף הוּא מִבֵּיתוֹ שֶׁל אֲבִימֶלֶךְ רַבִּי חָמָא אָמַר, לְשִׁבְעָה שְׁלֵמִים שֶׁהֵם תִּשְׁעָה מְקֻטָּעִים, רַבִּי הוּנָא בְּשֵׁם רַבִּי חִזְקִיָה, בַּחֲצוֹת הַיּוֹם נוֹלָד, נֶאֱמַר כָּאן מוֹעֵד, וְנֶאֱמַר לַהֲלָן, (דברים טז, ו) "כְּבֹא הַשֶּׁמֶשׁ מוֹעֵד צֵאתְךָ מִמִּצְרַיִם. (בראשית כ ג) וַיִּקְרָא אַבְרָהָם אֶת שֶׁם בְּנוֹ הַנּוֹלַד לוֹ אֲשֶׁר יָלְדָה לוֹ שָׂרָה יִצְחָק, יָצָא חֹק דְּרוֹרִיָּה לָעוֹלָם יִצְחָק י' עֲשָׂרָה, כְּנֶגֶד עֲשָׂרָה דִּבְּרוֹת שֶׁעֲתִידִין בָּנָיו לְקַבֵּל. צ' תִּשְׁעִים "וְאִם שָׂרָה הֲבַת תִּשְׁעִים שָׁנָה תֵּלֵד". ק' מֵאָה (שם) "הַלְּבֶן מֵאָה שָׁנָה יִוָּלֵד". ח' שְׁמוֹנָה, כְּנֶגֶד שְׁמוֹנָה יְמֵי הַמִּילָה. (בראשית כ ד) וַיָּמָל אַבְרָהָם אֶת יִצְחָק בְּנוֹ בֶּן שְׁמֹנַת יָמִים כַּאֲשֶׁר צִוָּה אֹתוֹ אֱלֹהִים, וְהֵיכָן דִּבֵּר, (בראשית יז, יב) "וּבֶן שְׁמֹנַת יָמִים יִמּוֹל לָכֶם כָּל זָכָר".