So, I am solving EGMO and had a confusion on this problem;
A circle has center on the side AB of the cyclic quadrilateral $ABCD$. The other three sides are tangent to the circle. Prove that $AD + BC = AB$.
My question is ;
Is it necessary that the center of circle is the midpoint of $AB$? Does it matter?
As I was able to solve most of the other problems, and from what I have heard, this is one of the easier problems so I shouldn't be having much trouble with it but I don't know why before starting the problem (at 2 in the night), I had this confusion in my mind so now I can't move past.
I am sorry if this is a dumb question, but please please clear my confusion.