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