Circularity and Evidence for Jesus’ Resurrection

Hello Dr. Craig,
I am a second year undergrad student at UCLA and have been an avid reader of your work since high school. I cannot express to you how powerful it is the work you are doing for the Kingdom. The example you have set in glorifying the Lord with your mind has been a source of great encouragement for me.
The lack of intellectual rigor that has pervaded the church saddens me deeply. Too often I find that Christians adhere to their belief purely through emotional experience. While they may be justified in this belief by the witness of the Holy Spirit, when tasked with explaining their belief to skeptics or appealing rationally to seekers, they are either unable to defend their beliefs with evidence or caught in the cycle of circular reasoning by using scripture to prove scripture.
I am a part of the Intervarsity leadership team here at UCLA and I hope to introduce and defend your apologetics work through seminars in the near future.
On to the actual question..
1. In your defense of the question "Does God Exist?", one of your standard five arguments from the theist point of view is "The Resurrection of Jesus". In this argument, you explain that the historical Jesus came on the scene with an unprecedented sense of divine authority and that Jesus claimed to be God and carried out a ministry of miracle working. You say that the supreme confirmation of Christ's claim was his resurrection from the dead. If Jesus really did rise from the dead, then it would seem that we have a divine miracle on our hands, and thus evidence for the existence of God. You explain three established, historical facts that you contend are best explained by the resurrection of Jesus and thus provide evidence for the existence of God. If this argument is sound, it would seem that the resurrection of Jesus is evidence for God's existence.
2. In some of your work (and I believe most recently in your Defenders: Doctrine of Christ (Part 24) podcast), you defend the Resurrection Hypothesis, that is, the hypothesis that God raised Jesus from the dead. As part of your argument for this hypothesis, you use probability calculus to show that while the Resurrection Hypothesis based on the background information alone is very improbable, once we are given the specific evidence, the Resurrection Hypothesis becomes much more probable. One aspect of the specific evidence you give is the probability of the existence of God. While it is highly improbable that Jesus rose from the dead naturally, if God exists then it is not at all improbable that God would raise his son from the dead to fulfill his plan for the universe.
So for the first argument stated, you contend that the resurrection of Jesus serves in itself as evidence for God's existence. In your Resurrection Hypothesis, you appeal to the evidence for the existence of God as a part of the specific evidence used to show that the Resurrection Hypothesis is more probable than not.
Are these arguments not then circular reasoning?
Please point out to me if I am wrong in my conclusion here, but if I understand these two arguments correctly and they do indeed use circular reasoning, it would not follow that the Resurrection Hypothesis is invalid, rather it would just show that the resurrection of Jesus could not in itself be evidence for the existence of God.
Again, thank you for everything you are doing for the Kingdom through your work and I want you to know that the impact of your work has significantly influenced me and eventually, I hope, the UCLA campus.
In Christ,
United States