Answer: this problem has only trivial solutions, with all points on the same line. x=5 or x=7/5.
Step-by-step explanation:
There are three triangles, and three unknowns: x, y=length of middle segment, and z=cos(angles marked with red arc).
We need
[tex]\cos(2\gamma)=(2\cos(\gamma)^2-1)[/tex]
and law of cosines,
[tex]c^2=a^2+b^2-2ab\cos(\gamma)[/tex]
The three equations are
[tex](2x-1)^2=9^2+y^2-2(9yz)[/tex]
[tex](3x)^2=15^2+y^2-2(15yz)[/tex]
[tex](3x+2x-1)^2=9^2+15^2-2(9\times15(2z^2-1))[/tex]
See attached image for solution.
