In the \(xy\)-plane, the circle \(C\) centered at the origin \(O\) is intersected by a line \(l\) at two points \(A\) and \(B.\) A line from \(O\) is drawn to \(AB\) intersecting \(AB\) at point \(D,\) such that the product of the slopes of \(OD\) and \(AB\) is \(-1.\) If the line \(l\) does not pass through origin and the coordinates of point \(D\) are \((1, -1),\) what is the radius of the circle?

1. The \(x\) intercept of line \(l\) is \(2\)

2) The product of the \(x\) coordinates of points \(A\) and \(B\) as well as the product of the \(y\) coordinates of points \(A\) and \(B\) is zero

The OA is B