(x,y)

(h,k)

(x,k)

r

x-h

y-k

k-y

h-x

Draw a circle with center
and radius

(h,k)

r

then the segment of length

r

starting at 

(h,k)

intersects the circle at

(x,y)

We now find the intersection
of the line through
parallel to the x axis, and the
altitude dropped from

(h,k)

(x,y)

 Draw Parallel Line 

 Reset 

 Draw Altitiude 

We now apply the 
Pythagorean Theorem

(x-h)^2

+

(y-k)^2

=

r^2

(h-x)^2

(k-y)^2

 Next 

 Next 

A = (1.94, 2.2)
radius = 4.3 (slider from 0 to 5, step 0.1)
c = Circle(A, radius)
B = Point(c)
a = OrthogonalLine(B, xAxis)
b = Segment(A, B)
d = OrthogonalLine(A, yAxis)
C = Intersect(a, d)
e = Segment(B, C)
f = Segment(A, C)
step = 1 (slider from 1 to 6, step 1)
D = Point(e)
g = Segment(B, D)
E = Point(f)
h = Segment(A, E)