Question

1. find x, given the tangent line.

Explanation:

Step1: Use Pythagorean theorem

Since the line is tangent to the circle, the radius is perpendicular to the tangent. So, we have a right - triangle with sides \(x\), \(5\) and hypotenuse \(13\). By Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), here \(a = x\), \(b = 5\), \(c = 13\). So \(x^{2}+5^{2}=13^{2}\).

Step2: Solve for \(x\)

$$
LATEXBLOCK0
$$

Answer:

\(x = 12\)