Answer:
[tex]\large\boxed{x=2\sqrt{181}\approx26.91}[/tex]
Step-by-step explanation:
If AB is a tangent of a circle, then the angle B is right angle. Therefore the triangle ABC is a rigth triangle.
BC and x are the radius of a circle. Therefore BC = x.
Use the Pythagorean theorem:
[tex]BC^2+BA^2=AC^2[/tex]
We have
[tex]BC=x,\ BA=80,\ AC=82[/tex]
Substitute:
[tex]x^2+80^2=82^2[/tex]
[tex]x^2+6400=6724[/tex] subtract 6400 from both sides
[tex]x^2=724\to x=\sqrt{724}\\\\x=\sqrt{4\cdot181}\\\\x=\sqrt4\cdot\sqrt{181}\\\\x=2\sqrt{181}[/tex]
