It's not clear what you mean by "model". Do you mean to shade the region? Or calculate points on the periphery? Or what?

You could think of moving the point {x2, y2} to the origin. (See the Mathematica GeometricTransformation and Translate routines). Then you could always translate your resulting expressions back.

There is a problem in that there is nothing to guarantee that {x1, y1} and {x3, y3} lie on the curve. At best they can be used to give the direction of the two straight lines and thus determine an angle for B. I think there is a VectorAngle routine or you could use a trigonometric expression.