To determine the radius of the circle given by the equation [tex]\(x^2 + y^2 = 144\)[/tex], we follow these steps:
1. Recall the standard form of the equation of a circle centered at the origin, which is [tex]\(x^2 + y^2 = r^2\)[/tex], where [tex]\(r\)[/tex] is the radius of the circle.
2. Compare this standard form with the given equation [tex]\(x^2 + y^2 = 144\)[/tex].
3. Observe that in the given equation, [tex]\(r^2 = 144\)[/tex].
4. To find [tex]\(r\)[/tex], take the square root of both sides of the equation [tex]\(r^2 = 144\)[/tex]: [tex]\[
r = \sqrt{144}
\][/tex]
5. Calculate the square root of 144: [tex]\[
\sqrt{144} = 12
\][/tex]
Thus, the radius of the circle is [tex]\( \boxed{12} \)[/tex].
