An infinite number of circles can be drawn through two given points. If we consider any two points on a plane, there are an unlimited number of circles that can pass through them. If we start drawing the circles by taking the two points to firstly function as the diameter of the first circle, we can then move up along the circumference of the circle such that the points become a chord of the circle instead. In a similar way, we can keep moving down the circumference to make the points become chords of varying lengths and draw an infinite number of circles through the same two points.