4.3.2 let ii be a fixed circle of center o and radius p, and let p be any point in the plane of ii. then the point p on the ray op such that op op p2 is called the inverse of p with respect to circle 11.22 circle ? is called the crcle ofinversion, point o the ons inversion, and p2 the power of inversion. there is set up a one-to-one correspondence between the points of the plane of il; to every point t corresponding point. the points of a curve c will invert into the points of a curve c', called the inverse of c. establish the following theorems concerning this inversion transformation. nl (a) if p is the inverse of p, then p is the inverse of p. (b) a point inside the circle of inversion inverts into a point outside the circle of inversion; a point outside the circle of inversion inverts into a point inside the circle of inversion; a point on the circle of inversion inverts into itself. (c) a straight line through the center of inversion inverts into itself (d) a circle orthogonal to the circle of inversion inverts into itself. (e) if p, p and q, q' are any two pairs of inverse points that do not lie on the same diameter of the circle of inversion, then these four points lie on a circle (f) a straight line that does not pass through the center of inversion inverts into a (g) a circle that does not pass through the center of inversion inverts into a circle (h) any circle through a pair of inverse points p and p cuts the circle of (i) a given circle may be inverted into itself by the use of any given exterior circle passing through the center of inversion, and conversely. that does not pass through the center of inversion. inversion orthogonally