A circle with center (0, 0) passes through the point (5, 12). How do you find the radius of the circle?

Jan 29, 2016

The radius is simply the distance from the center to the edge, and we can use Pythagoras' Theorem to calculate that for this circle the radius is $13$ units.

Explanation:

The radius is simply the distance from the center to the edge. We know the center is at $\left(0 , 0\right)$ and that the edge passes through the point $\left(5 , 12\right)$. We need to find the distance of this point from the center, using Pythagoras' Theorem:

${a}^{2} = {b}^{2} + {c}^{2}$

We can do this because $5$ and $12$ are the $x$ and $y$ values respectively of the point on the Cartesian plane. The $x$ and $y$ axes are at right angles $\left({90}^{o}\right)$ to each other, so we have a right-angled triangle when we add the radius from $\left(0 , 0\right)$ to $\left(5 , 12\right)$, which is the hypotenuse of the triangle.

${a}^{2} = {b}^{2} + {c}^{2} = {5}^{2} + {12}^{2} = 25 + 144 = 169$

Taking the square root of both sides, $a = 13$ and this is the radius of the circle.