Double slit experiment (geometric maths problem)

[Generic Turtle]

I understand the experiment and the trigonometry involved except for one statement.

Why is BP-AP=BD in this diagram

http://www.citycollegiate.com/interference2.htm

How do you know this/ work it out.

Many thanks

 

[mfb]

PA = PD to a very good approximation as AD is extremely small compared to both.

 

[Generic Turtle]

Thank you