Question

Given a center circle alpha = 0. and OA is between L explain what the image of l under inversion in alpha is (drawing to follow)

Answer 1

isn't this one of the circle inversion theorems?

Answer 2

Maybe it's
under the inversion with respect to a circle a straight line l that has no common points is transformed into a circle alpha passing through 0?

Answer 3

or let alpha be a circle in radius r center O. For any point P not equal to 0 the inverse of P' of P with respect to alpha is the unique point P' on ray OP such that (line OP)(line OP') = r^2 (where line OP denotes the length of segment OP with respect to a fixed unit of measurement

Answer 4

P = P' if and only if P lies on the circle of inversion alpha
If P is inside of alpha then P' is outside of alpha and if P is outside of alpha then P' is inside of alpha. (P')' =P