Ncb+NBC =90

∠NCB+∠MCA=90

NBC =∠MCA

Similarly ∠NCB=∠MAC

AC=BC

△NBC?△MCA

NB=MC，NC=AM

MC+NC=AM+NB

MN=AM+BN

The situation of the second question is shown in the picture (please don't mind if the picture is not good)

And △ NBC △ MCA.

NB=MC，NC=AM

But at this time MN=CM-CN=NB-AM.

On the other hand, AM is greater than BN.

At this time, MN=CN-CM=AM-BN.

To sum up, if MN and AB intersect.

There is an absolute value of MN=AM-BN.