Umar (may Allah be pleased with him) fighting the polytheists at the beginning of his Islam

It is narrated from Sayyiduna Abdullah bin Umar (may Allah be pleased with them both) that Sayyiduna Umar (may Allah be pleased with him) kept fighting the polytheists in the mosque of Makkah (the Ka'bah). He fought them from morning until the sun was overhead; then he became exhausted and sat down. Meanwhile a man with a handsome face came, wearing a red cloak and a Qumasi shirt. He came and pushed the people away and asked: What do you want from this man? They said: Nothing, except that he has turned away from the religion of his forefathers. He said: Then he has chosen an excellent religion for himself; leave him to what he has chosen. Do you think that Banu Adi would be pleased for Umar to be killed? By Allah, Banu Adi would never be pleased with it. On that day Sayyiduna Umar (may Allah be pleased with him) said: O enemies of Allah, if our number reached three hundred, we would drive you out of here. (Sayyiduna Abdullah bin Umar said:) Later I asked my father: Who was the man who pushed the people away from you that day? He said: That was al-As bin Wa'il, the father of Amr bin al-As.
This hadith is sahih (authentic) on the condition of Imam Muslim, but the two Shaykhs (Bukhari and Muslim) did not record it.

It is narrated from Sayyiduna Abdullah bin Abbas (may Allah be pleased with them both) that when Sayyiduna Umar (may Allah be pleased with him) accepted Islam, the polytheists said: Today our match has been made against us (that is, with the Muslims' strength increasing, our power has been left at half).
This hadith has an authentic (sahih) chain, but the two Shaykhs (Bukhari and Muslim) did not record it.