Inversions

Inversions of a point, circle and line

Circle

P

P'

Point

P

P'

Line

E = (1.9149371357279685, -0.7215939814568043)
D = (2.0903559040982587, 0.5666771031026934)
d = Circle(D, E)
O = Intersect(xAxis, yAxis)
B = Point(xAxis)
c = Circle(O, B)
P = Point(d)
P' = Mirror(P, c)
a = Segment(O, P)
b = Segment(O, P')
OP = Distance(O, P)
OP' = Distance(O, P')
ks: OP * OP'
sqrks: sqrt(ks)
loc1 = Locus(P', P)
e = false
A = (1.8791347690671087, 0.4240817516907127)
A' = Mirror(A, c)
f = false
C = (1.5569134691193705, -7.130217613750724)
F = (13.872927600455196, 6.080855684106578)
g = Line(C, F)
G = Point(g)
G' = Mirror(G, c)
loc2 = Locus(G', G)
h = Segment(O, G')
i = Segment(O, G)
j = false
text1: "OP.OP' = " + OP + "×" + OP' + " = " + ks + " = " + sqrks + "²"
OA = Distance(O, A)
OA' = Distance(O, A')
OG = Distance(O, G)
OG' = Distance(O, G')
text2: "OP.OP' = " + OA + " × " + OA' + " = " + ks + " = " + sqrks + "²"
text3: "OP.OP' = " + OG + " × " + OG' + " = " + ks + " = " + sqrks + "²"