1) AR=12, AN=x. AN·AM=AR·AP, x·4=12·5, x=15.

The problem states that AN = x, AM = 4, AR = 12, and AP = 5. The intersecting secants theorem states that AN * AM = AR * AP. Substituting the given values, we get x * 4 = 12 * 5. This simplifies to 4x = 60. Dividing both sides by 4 gives x = 15.