After healing the lame man, Peter could have emphasized the healing or recounted several occasions when the risen Christ met individuals and groups of people. Instead, Peter preached on Deuteronomy 18:15ff and Genesis 12:3 (see Acts 3:22, 25). Peter followed the pattern of preaching he had begun at the first Christian Pentecost when he preached on Joel 3:1-5; Psalm 16:8-11; and Psalm 110:1 (see Acts 2:17ff, 25ff, 34f). Peter was inspired by Jesus to preach the Scriptures, for that is what Jesus did throughout His public ministry and especially right after His resurrection (see Lk 24:27, 45).
To be powerful witnesses for the risen Christ, we need to devote ourselves to the Church's teaching of God's word (see Acts 2:42), sow bountifully the seed of God's word (see 2 Cor 9:6), and "day after day, both in the temple and at home" never stop "teaching and proclaiming the good news of Jesus the Messiah" (Acts 5:42). Jesus charges us "to preach the word, to stay with this task whether convenient or inconvenient — correcting, reproving, appealing — constantly teaching and never losing patience" (2 Tm 4:2).
"Remember that Jesus Christ, a descendant of David, was raised from the dead. This is the gospel I preach" (2 Tm 2:8). "There is no chaining the word of God!" (2 Tm 2:9)