Biomechanics of feet

I noticed today that the arch of my left foot is substantially flatter than that of my right. Some idle poking around the internet suggests that flat feet leads to out-of-plane stress on the knee joints, which may be behind my left knee's persistent complaints. That improved a little after I started bicycling regularly, which argues that muscle strength can play a role in the solution. That, in turn, leads me to arch-strengthening exercises. After doing a set of ten, my feet hurt.

If I can remember to keep up with this for a couple of weeks, I'll post a progress report.