Find the measure of x.

Question

asked Apr 16, 2020 202k views

1 Answer

Peter Walser · Answer 1 · 2020-04-20T15:42:19+0000

Answer:

$\large\boxed{x=2√(181)\approx26.91}$

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

$x^2=724\to x=√(724)\\\\x=√(4\cdot181)\\\\x=\sqrt4\cdot√(181)\\\\x=2√(181)$