If the back compensation angle PAB= foot PCB, it can be proved that:

Because angle PAB plus pin PCB is equal to 180, and angle PAB= pin PCB.

So the angle PAB= feet PCB=90 degrees.

Because angle b is divided equally by BN.

So angle CBN= angle NBA

BP is the public party.

So triangle CBP is equal to triangle PBA.

The corresponding sides of congruent triangles are equal.

So PA=PC