So I was given this by a student at my job, I tried setting up a system using a couple right triangles but I have like 4 unknowns and I doubt the teacher wants them to do a 4 by 4? I know I am totally brain farting and am forgetting one piece of information.
Also it didn't specify the point is the CENTER, but IF it were the center, would that imply $x = 4$?
and it looks like the figure inside the circle is a kite? thanks for any help and sorry for my huge brain fart. I am currently preparing for the GRE subject and I feel stupid when I get stuck here.
ALSO, they gave me that the answer is $x = 2$. I don't like working backwards though knowing the answer specially since I am teaching it to a high school student.
If the point were the center, then since a perpendicular from the center of a circle to a chord always bisects the chord, $x=4$.
If the point were not the center, and was an arbitrary point inside the circle, then $x$ could be anything, and the diagram would still be possible.