Note: I give two explanations for this problem (both are the same thing) to make the problem more understandable.
Let triangle △ABP0 be an obtuse isosceles triangle with ∠B=36∘, ∠P0=108∘, and segment AB=2015.
Here is a general description of the pattern.
Angle ∠BP0A is trisected by segments P0P1 and P0D1 where P1 and D1 are on side AB and BP1<BD1
Next, angle P0P1B is trisected by segments P1P2 and P1D2 where P1 and D1 are on side P0B and P2B<D2B.
Here is an explicit description
Now, given the pattern above, let the point Pn and Dn be the points resulting from the trisection of ∠Pn−2Pn−1B with BPn<BDn.
If P6P7P9P10 can be expressed as (c−a+b)k where b is square free and a,c are co-prime positive integers and k is an integer, what is the value of abck?