Coming back after a long time.....
The question:
Prove that a point can be found which is equidistant from each of the following four points:
A (a m1, a/m1),
B (a m2, a/m2),
C (a m3, a/m3), and
D (a/m1m2m3, a m1m2m3)
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1 Answers
62xy=a2
(x-h)2+(y-k)2-r2=0
now substitute x=a2/y
(a2/y-h)2+(y-k)2-r2=0
(a2-hy)2+(y2-yk)2-(yr)2=0
y4-2ky3+y2(1+h2-r2)-2a2hy+a4=0
The product of the roots is a4
so if three of the y coordinates are a/m1, a/m2, a/m3 the 4th will automatically be am1m2m3..
Similarly the x coordinate can also be found..
Hence the proof [1]
