Question

Find the measure of x.

Answer 1

Answer:

$\large\boxed{x=2\sqrt{181}\approx26.91}$

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:

$BC^2+BA^2=AC^2$

We have

$BC=x,\ BA=80,\ AC=82$

Substitute:

$x^2+80^2=82^2$

$x^2+6400=6724$            subtract 6400 from both sides

$x^2=724\to x=\sqrt{724}\\\\x=\sqrt{4\cdot181}\\\\x=\sqrt4\cdot\sqrt{181}\\\\x=2\sqrt{181}$