On the side $A D$ of the inscribed quadrilateral $A B C D$, there is the center of the circle that touches the other three sides of the quadrilateral. Find $A D$, if $A B=2$ and $C D=3$.

#
Prove that $A D=A B+C D$.

## Answer

5. 

Translate the text above into English, please keep the original text's line breaks and format, and output the translation result directly.