Are the gospel accounts of Jesus reliable?

Are the gospel accounts of Jesus reliable?
Secular historians recorded the general facts of Jesus' life, but his close associates made more detailed reports based on direct eyewitness testimony. These are called the four gospels, the first four books of the New Testament. How can we be sure these biographies of Jesus are accurate?

When historians try to determine if a biography is reliable, they ask, "How many other sources report the same details about this person?" Here's how this works. Imagine you are collecting biographies of President John F. Kennedy. You find many describing his family, his presidency, his handling of the Cuban Missile Crisis, and almost all of the biographies report similar facts. But what if you found one biography reporting that JFK lived ten years as a priest in South Africa? The other biographies had him in the U.S. at the time; a sensible historian would go with the accounts that agree with one another.

Regarding Jesus of Nazareth, do we find multiple biographies reporting similar facts about his life? Yes. While they don't redundantly cover all of the same information, the four gospels tell essentially the same story:

Two of the gospels were written by the apostles Matthew and John, men who knew Jesus personally and traveled with him for over three years. The other two books were written by Mark and Luke, close associates of the apostles. These writers had direct access to the facts they were recording. The early church accepted the four gospels because they agreed with what was already common knowledge about Jesus' life.
Each of the four gospel writers made a very detailed account. As you would expect from multiple biographies of a real person, there is variation in the style but agreement in the facts. We know the authors were not simply making things up, because the gospels give specific geographical names and cultural details that have been confirmed by historians and archaeologists.

Jesus' recorded words leave out many topics the early church would have liked a statement on. This indicates that the biographers were honest, not putting words in Jesus' mouth to suit their own interests