The Islamic Dilemma is in Quran 5:47.
It says: "And let the people of the Gospel judge by what allah has revered therein.
And whosoever does not judge by what allah has revealed, then it is those who are defiantly disobedient."

 The Dilemma is where you're stuck with only 2 options and both of them cause a problem.  If Mohamed is telling the people to go to this Gospel book and this book is Inspired from God (The Bible) then there are only 2 possibilities.

One is that the Bible is really the Inspired word of God. if the Bible is really the Inspired word of God, then Jesus Christ died on the Cross for sins and rose  from the dead and claimed to be God, If those things are true, then Mohamed was a false prophet because he rejected all of these, So that's 1 possibility. The Bible is true in which case Mohamed was a false prophet.

The other Alternative is that the Bible is not Inspired, If that's the case, then Mohamed is telling people to go to a book that is false and not the word of God. That will mean that Mohamed was a false prophet. So since Mohamed told people to go to this book, if it is the word of God, then he is a false prophet because he is telling everyone to go to a false corrupt book.

So by appealing to the Bible, Either way you want to look at it, Mohamed turns out to be a false prophet. Mohamed never believed the Bible was corrupted, everything that he says indicates that the Bible is the true word of God. In Sunnan Abu Daud no. 4464, Mohamed put his hand on the Torah and said, I confirm that this is the word of God.

In Quran 15:91, It says the Koran was ripped into shreds, now on the other hand, Muslims say the Bible words were exchanged but the Koran words were ripped into shreds according to the Koran itself. Mohamed Authenticates the Bible as God's Inspired Word.