Reflection Loci: Cardioid, Deltoid and Nephroid

Click on the arrows to show the stages of the construction

A = Point(a)
B = Point(a)
c = Circle(A, B)
G = Point(c)
b = Ray(B, G)
d = OrthogonalLine(G, a)
D = Intersect(a, d)
e = Segment(G, D)
D' = Mirror(D, b)
f = Segment(D, D')
loc1 = Locus(D', G)
D'' = Mirror(D', e)
g = Segment(D', D'')
loc2 = Locus(D'', G)
D''' = Mirror(D'', b)
h = Segment(D'', D''')
loc3 = Locus(D''', G)