ABC is a triangle with AC = 1, AB = c/b and BC = a/b.
Q is a variable point on AC such that CQ = x and QA = 1 – x.
The perpendiculars from A and C to BQ (extended if necessary) are $d_2$ and $d_1$ respectively.
p is a given length of reasonable size (like $p > d_1$ and $p>d_2$).
If $d_1^2 + d_2^2 = p^2$, find the location of Q (or equivalently x) in terms of (some of) the given unknowns.
I have transformed the question to the following figure. But that still leads me to nowhere. Any suggestion (either continuing or starting from the very beginning)? 
