Question

What is the value of x?

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x =
​​

Answer 1

Answer: this problem has only trivial solutions, with all points on the same line. x=5 or x=7/5.

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*15(2z^2-1))`

See attached image for solution.