Let P be a point in triangle ABC such that angles APB, BPC, and CPA are all 120 degrees. Can lines AB, AC, BC, PA, PB, and PC all have integral lengths?
(In reply to
re(3): on another look by Nishant)
For
a^2=y^2+z^2+yz
b^2=x^2+z^2+xz
c^2=x^2+y^2+xy
consider
a=399
b=511
c=455
x=325
y=195
z=264
The left and right sides of eq. 1 are each 159,201; of eq. 2 are 261,121; and of eq.3 are 207,025.
Why in solving the quadratic, are you seeking a double root?

Posted by Charlie
on 20070413 16:46:25 