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A Point in a Triangle (Posted on 2007-04-12) Difficulty: 4 of 5
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?

See The Solution Submitted by Brian Smith    
Rating: 3.0000 (1 votes)

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re(4): on another look | Comment 7 of 8 |
(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 2007-04-13 16:46:25
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