The PC is at station 3+35. By foot of perpendicular, I suppose you want to know how far it is from station 3+35 to station 4+00, 65 feet, a straight distance and not along the curve?. I am not sure I am understanding correctly.

The radius of the curve can be gotten from . I am assuming you mean the degree of the curve is 4 degrees and the Delta angle is 27.4 degrees?.

The angle deflection can be gotten from . That is degrees per foot.

Multiply by 65 to find the angle of deflection at 65 feet and we get

1.3 degrees. That is the angle we would turn with our transit to fix that station 4+00.

That is the length of the short chord. Which is 65 feet for all intents and purposes.

Remember, the delta angle is 27.4. If you were to set up the transit, back sight, turn over and turn a deflection of half the delta, that should put you on your PT(point of tangency).

I hope I understood your problem correctly. I have laid out many roads and bridges, so if I know what you mean I should be able to help.