Can you solve this pier puzzle?

Heh, I actually paused to solve this. At first linear interpolation came to mind since the pier point seems linearly dependent on the distances of the two towns, and then reflecting one town made sense. So doing that, I wanted to end up with the location of the point on the line on an equation:
D = a/(a+b) * p, where a,b are the distances of A and B cities from the shore, p is the distance of the two points on the reflection triangle and D the shoreline intersection. Taking the actual distance between a and b, and then intersecting to the shoreline seemed inconvenient and pointless, so by mapping that distance to the projection of the points, I got the linear interpolation of D = a/(a+b) * p, where D is distance of the pier from a's projection, and p the distance of the two projections, aka the shoreline in between a and b. Fun stuff!

Edit: Yeah, I did what Derek did , without the calculus stuff!