How many circles can be drawn through two given points?

Question

Vedantu Content Team · Accepted Answer

Hint:Here,first we can give a short description on a circle regarding diameter and chord. Then, identify the number of circles drawn through a single point. Similarly, for two points we have to find the number of circles drawn. We can also consider the graph for better understanding.

Complete step-by-step answer:
Here, we have to find the number of circles that can be drawn through two given points.
First we will discuss about circle.
We know that a circle is the set of points in a plane that are equidistant from a given point. The distance from the centre is called the radius and the point is called the centre. The longest distance from one end of a circle to the other is called diameter. A chord of a circle is a straight line segment whose endpoints both lie on the circle.
We know that through a single point we can draw infinitely many circles. If a point is given then through that point we can construct an infinite number of circles.
Now, consider two points. If two points are given then similarly, like a single point we can draw an infinite number of circles.
That is, starting from the two points as a diameter, we can draw a circle. As the circle is moving up it becomes a chord to the next circle with a bigger diameter. Then, again as the circle is moving up the bigger diameter also becomes a chord to the next circle. This process will go on. In such a way, we can draw an infinite number of circles passing through two points.
We can also draw a figure for better understanding.
Here, we can see through two points A and B, we can draw as many numbers of circles as we want.

Note: here, you can draw an infinite number of circles from two points. The two points you have chosen will be equidistant from the centre of the circle. That is the distance of the two points from the centre of the circle will be the same. If you join these two points, it can be a diameter to one circle and chord to all other circles.And also we can draw an infinite diameter and chord for a given circle.