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

1 Answer
Jan 29, 2016

Answer:

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.