Circumscribed Circle of a triangle

The local town hall is getting a new clock. The Mayor wants it to be as big as possible so it can been seen by everyone. As the town engineer you have been asked to make this happen. Using the construction of a circumscribed circle in a triangle,you can to fit the largest clock face possible given the triangular shape of the roof. Follow the steps to see how.

Move the point E around and see how the circle still remains circumscribed in the triangle. [i]For you to do. Construct a triangle of any shape and try to circumscribe a circle in it using the steps highlighted. [/i] [b]Note: You do not need to bisect the same angles in this applet, any two angles will do![/b]