Do you have a program like "Geometer's Sketchpad"

There is no way I could have cracked this problem without it.

If you made a nice sketch you will notice that the ray MC passes through the point O (circumcenter of triangle ABC). I thought this was how I constructed my sketch. But no, the way point M is constructed it is forced to lie on line CO. After seeing this I was hoping to drop the difficulty to 3 or 2.

I have started to put together my solution. Should have it out in a couple of days.

Hope the above helps.