Let's say I have a quadrilateral that is convex and I know the points that are forming it. How can I know if the quadrilateral is circumscribed? Is it true that a quadrilateral is circumscribed if and only if the sum of opposite sides are equal?
In my case, picture above, only if $AB+CD=AC+BD$?
It's true. It's Pitot's Theorem and its converse.
See http://www.cut-the-knot.org/Curriculum/Geometry/Pitot.shtml