Bended line without lenght changes.

Hello everyone! Problem:I have a line, with start and end point. in a second step I have to scale this line(make it longer, with a fixed percent), third step I would like to bend the scaled line to curve in a  way when the start and the end points are same with the original line, and the banded curve lenght must be a same as the scaled one, and also it must be a  a simmetrical curve.(maybe it can be a part of a circle).
If somebody know the solution could help to me?