Alhazin was a Muslim mathematician at the turn of the millenium. The problem of Al Hazin is to find the image of a brilliant point when reflected off of a circle. Essentially, this entails finding a point (A) on the circumference of a circle such that segments from two other points in the plane to A make equal angles with the normal of the circle at that point. This process boils down to finding the roots of a fourth degree polynomial.
The Problem of Alhazin