Brownian Motion in Circles Puzzle
Suppose the starting point of a particle undergoing Brownian motion in 2 dimensions is chosen uniformly at random on an imaginary circle C_1. Suppose there is a solid circle C_2 completely inside C_1, not necessarily concentric. Show that the particle hits the boundary of C_2 with uniform distribution.
Book: I strongly recommend the book by Steven Shreve for understanding Brownian Motion and its applications in Financial Modelling (Its expensive! Flipkart Link: Stochastic Calculus for Finance II)
Update (4th Feb 2013):
Solution posted by me in comments!