How many circles can be drawn passing through
A) one given point?
B) two given points?

Hint:
Here, we have to find the number of circles that can be drawn through one point and two points. A circle is a shape consisting of all points in a plane that are a given distance from a given point, the centre.

Complete step by step solution:
a) We want to find the number of circles that can be drawn passing through one given point.
We can draw infinitely many circles passing through one given point if the given point is not a center. But if it is a center we can draw only one circle.
Therefore, we can come to a conclusion that when the given point is a center, we can draw only one circle. When the given point is not a center, we can draw infinitely many circles.

b) We want to find the number of circles that can be drawn passing through two given points.
We can draw infinitely many circles passing through two given points.
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. In such a way, we can draw an infinite number of circles passing through two points.

Therefore, Infinitely many circles can be drawn through two given points.

Note:
We should also know the properties of a circle. The diameter of a circle is the longest chord of a circle. The chords that are equidistant from the centre are equal in length. The distance from the centre of the circle to the longest chord (diameter) is zero. The perpendicular distance from the centre of the circle decreases when the length of the chord increases. Circles having different radius are similar. We should know these properties while constructing a circle.