The answer was pretty obvious but I had to go synthetic for a proof.
A=(0,0)
B=(a,0)
C=(a,d)
D=(0,d)
P=(x,y)
a=sqrt(x^2+y^2)
b=sqrt((xa)^2+y^2)
c=sqrt((xa)^2+(yd)^2)
d=sqrt(x^2+(yd)^2)
a^2 + c^2 = b^2 + d^2 = x^2 + (xa)^2 + y^2 + (yd)^2
The above is the relationship between the four lengths. Solving for d gives the requested solution:
d = sqrt(a^2  b^2 + c^2)

Posted by Jer
on 20170228 11:31:26 