Question Video: Determining How Many Circles Pass Through One Point Mathematics

Video Transcript

How many circles can pass through one point?

Let’s recall that we can mathematically define a circle as a set of points in a plane that are a constant distance from a point in the center. We’re asked how many circles can pass through one point. So, let’s take a point on the screen and let’s label it with 𝑃. So, how could we draw a circle which passes through the point 𝑃?

Well, to do that, let’s take another point here, which will be the center of a circle. If we take this center point to be the point 𝑀 sub one, then the distance between 𝑃 and 𝑀 sub one would be the radius of the circle. So, here, for example, is one circle which passes through the point 𝑃. We could find another point, for example, here and then create another circle with this point, let’s call it 𝑀 sub two, as the center. And so, there is another circle, which also passes through point 𝑃.

You might realize that we could repeat this any number of times, for example, with smaller circles, larger circles, or, in fact, circles which don’t even fit completely on the screen. We could even draw a circle which passes through point 𝑃 and has a radius of 1000 kilometers. And so, of course, the number of circles that can pass through this point 𝑃 isn’t just the five circles that we have on the screen. In fact, there would be an infinite number.

And therefore, the answer is that there are an infinite number of circles which can pass through one point.