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((x-a)^2+y^2)
c=sqrt((x-a)^2+(y-d)^2)
d=sqrt(x^2+(y-d)^2)
a^2 + c^2 = b^2 + d^2 = x^2 + (x-a)^2 + y^2 + (y-d)^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)
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Posted by Jer
on 2017-02-28 11:31:26 |
Solution
