Question

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

Answer 1

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 `(0, 0)` and that the edge passes through the point `(5, 12)`. 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 `(90^o)` to each other, so we have a right-angled triangle when we add the radius from `(0, 0)` to `(5, 12)`, 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.