I received this geometry question as a challenge several months ago and decided to pull it back out. I managed to prove that the angle is less than 45 degrees, but I have no idea what do do overall to find the answer.
ADOC is a secant of a circle center O. A lies outside the circle and D and C lie on the circle. ABE is also a secant of Circle O and B and E are distinct points lying on the circle O. If AB = BC, compute, in degrees, the largest possible possible integer value of the measure of angle <CAE.