Question

Find the measure of x.

Answer 1

`\large\boxed{x=2√(181)\approx26.91}`

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=√(724)\\\\x=√(4\cdot181)\\\\x=\sqrt4\cdot√(181)\\\\x=2√(181)`