1.  What is special about the two circles below?

2.  Grab point D and move it along the line.  What do you notice about the circles?

3.  What do you notice about point F?

4.  Right click on point P and turn the trace feature on. What happens as we move point D?

5. Right-click on point P and turn off the trace feature. Now move F to another location farther way from line AB. 
 
6. Right-click on point P and turn the trace feature back on.  Again move point D along line AB. Compare and contast the figures formed by the first trace and the second trace.

7.  What geometric theorems were used to construct this document?  (Hint:  In the Algebra window click on open circles to display angles alpha and beta, line d, and segment c.)

A = (-2.18, -5.02)
B = (13.84, -5)
a = Line(A, B)
F = (7.14, -3.98)
D = Point(a)
b = OrthogonalLine(D, a)
c = Segment(F, D)
d = LineBisector(c)
P = Intersect(b, d)
e = Segment(D, P)
f = Segment(F, P)
g = Circle(D, P)
h = Circle(F, P)
α = Angle(P, D, A)
C = Midpoint(c)
β = Angle(P, C, D)