Circle Geometry; cyclic quadrilaterals
An illustration of the angle properties to be found in a cyclic quadrilateral.
Circle Theorems http://www.geogebratube.org/student/c89/m1462/yryy
This is a nice theorem to prove algebraically.
As a start to your proof you could mark the centre of the circle and
draw in the radii to the vertices of the quadrilateral.
A nice alternative is to draw the diagonals and use another popular circle theorem
that you can see illustrated here http://www.geogebratube.org/student/m1462