Actually this one's quite annoying me.

I can see a brutal approach - but I'm sure there's a simple approach based on a cyclic quadrilateral theorem (so that there's a point to part (a)) ..... Probably a theorem dealing with the case of one of the diagonals being a diameter of the circle that would lead to something along the lines of ... perhaps a special case that follows from Ptolemy's Theorem ....... Nothing I could find using google - I'll probably end up proving (or disproving) what I want myself .....