(a) In a quadrilateral ABCD, the sides AB and CD are parallel, and the diagonal BD bisects angle ABC. Let X be the point of intersection of the diagonals AC and BD. Show that the ratio AX:XC is the same as the ratio AB:BC.

There is also a follow up question, which I'm assuming requires the first question to be solved before it can be attempted. However, it may help to determine the best strategy, so here it is:

(b) In a triangle PQR, the length of each of the three sides is a positive integer. Point M lies on the side QR so that PM is the internal bisector of angle QPR. Also, QM=2 and MR=3. What are the possible lengths of the sides of triangle PQR?

Any help with either or both parts would be much appreciated.

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