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The equation of a circle centered at the origin is [tex]$x^2 + y^2 = 144$[/tex]. What is the radius of the circle?

A. 144
B. 72
C. 14
D. 12

Sagot :

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].

So, the correct answer is:
D. 12