Find x. Round to the nearest tenth if necessary. Assume that segments that appear to be tangent are tangent. Your help is much appreciated - thanks! :)

The radius of the circle 9/2, or 4.5 units.

Tangent lines are perpendicular to the radius.
Thus, we can form a right triangle, since x is a tangent segment.

The legs of the right triangle will be 4.5 and x.

The hypotenuse will be the sum of the 3 and the length of the radius. The hypotenuse is 7.5.

Look at the attached image to help you understand the visualization of the right triangle.

Use the Pythagorean theorem to find x.

[tex]x=\sqrt{7.5^2-4.5^2}[/tex]

[tex]x=\sqrt{36}[/tex]

[tex]x=6[/tex]

The answer is x=6. I hope this helps! :)