Question

Find x. Assume that segments that appear tangent are tangent.

Answer 1

Answer:

$x=40\ units$

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

segment BC is a tangent to the circle at point B  ---> given problem

AB is a radius of the circle

The tangent BC is perpendicular to the radius AB

Remember that

According to the Perpendicular Tangent Theorem, tangent lines are always perpendicular to a circle's radius at the point of intersection

so

The triangle ABC is a right triangle

Applying the Pythagorean Theorem

$AC^2=AB^2+BC^2$

substitute the given values

$41^2=9^2+x^2$

solve for x

$1,681=81+x^2$

$x^2=1,681-81$

$x=40\ units$