Question

What is the value of x? Enter your answer in the box. x = ​​

Answer 1

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

$\cos(2\gamma)=(2\cos(\gamma)^2-1)$

and law of cosines,

$c^2=a^2+b^2-2ab\cos(\gamma)$

The three equations are

$(2x-1)^2=9^2+y^2-2(9yz)$

$(3x)^2=15^2+y^2-2(15yz)$

$(3x+2x-1)^2=9^2+15^2-2(9\times15(2z^2-1))$

See attached image for solution.